# Archiv des Rhein-Main-Kolloquiums Stochastik

## Summer term 2022

July 22nd, 2022, 14.30 CET, Rhein-Main-Kolloquium Stochastik, Gutenberg-Universität Mainz

Eva Löcherbach (Université de Paris):

On conditional propagation of chaos for interacting systems of neurons in a diffusive regime

Matthias Hammer (TU Berlin):

The asymptotic speed of the maximal particle in on/off-Branching Brownian Motion

Simon Holbach (JGU Mainz):

(Self-)interacting diffusions and sampling algorithms for rare event systems

July 1st, 2022, 15:15 Uhr, Rhein-Main-Kolloquium Stochastik, Goethe-Universität Frankfurt

Functional Representation Theorems for Exchangeable Laws

Functional Representation theorems (FRTs) for exchangeable random objects exist for many types of data structures, for example sequences (de Finetti/Hewitt-Savage),
partitions (Kingman), hierarchical structures, graphs or more general array-like data structures (Aldous-Hoover-Kallenberg).  In this talk several known FRTs are presented and the language of category theory [vocabulary: cagegory, functor, natural transformation] is used to introduce an abstract concept of data structures, which allows for a unified formulation of many known FRTs. This leads to a conjecture about a "General FRT".  No knowledge of category theory is assumed to follow this talk, the concepts will be motivated by statistical practise.
This research is funded by the DFG project 502386356.

16:15 Uhr Kaffeepause

At the edge of a cloud of Brownian particles

The talk concerns a model for the motion of particles carried in a turbulent fluid in which a single particle moves according to an SDE of the form dX_t= \sigma dB_t + dW(t,X_t). Here, W is a Gaussian field, describing the environment, and B is an independent Brownian motion representing some additional diffusivity. We are interested in the behaviour at large times, but far from the origin.  There,  we find a transition which is analogous to that between weak and strong disorder for polymer models, and at the transition the stochastic heat equation appears.

Ort: Robert-Mayer-Str. 10, Campus Bockenheim, Frankfurt/Main, Raum 711 gr.

## Winter term 2021/2022, hybrid events or online via Zoom only

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January 14, 2022, 15 c.t. CET, Rhein-Main-Kolloquium Stochastik, Gutenberg-Universität Mainz, online via Zoom

15:15-16:15: René Schilling (TU Dresden)

16:15-16:45: Virtual coffee break

16:45-17:45:  Andreas Kyprianou (University of Bath)

René Schilling: Some martingales for Levy processes

We show the structure of all martingales of the form $f(X_t)- Ef(X_t)$ or $g(X_t)/E g(X_t)$ where $X_t$ is a Levy process. This is connected with Cauchy's functional equation and the Liouville theorem for Levy processes. (Joint work with Franziska Kühn)

Andreas Kyprianou: Asymptotic moments of spatial branching processes

We introduce a very general class of non-local branching particle processes and non-local superproesses for which the asymptotic moments can be computed explicitly as a function of time (our results are agnostic to either category of process). The method we use is extremely robust and we are able to provide similar results for the asymptotic moments of occupation functionals as a function of time.

Online via Zoom - No registration required for this event

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Friday, December 3, 2021, 3 pm CET ct,  Rhein-Main-Kolloquium Stochastik, Goethe Universität Frankfurt/Main, Online event via Zoom

15:15-16:15: Nina Gantert (TU München)

16:15-16:45: (virtual) coffee break

16:45-17:45: Paolo Dai Pra (Università degli Studi di Verona)

Nina Gantert (TU München)

Sharp concentration for the largest and smallest fragment in a k-regular self-similar fragmentation

Abstract: We study the asymptotics of the k-regular self-similar fragmentation process. For α>0 and an integer k≥2, this is the Markov process (I_t)_{t≥0} in which each It is a union of open subsets of [0,1), and independently each subinterval of It of size u breaks into k equally sized pieces at rate u^α. Let k^{−mt} and k^{−Mt} be the respective sizes of the largest and smallest fragments in I_t. By relating (I_t)_{t≥0} to a branching random walk, we find that there exist explicit deterministic functions g(t) and h(t) such that |mt−g(t)|≤1 and |Mt−h(t)|≤1 for all sufficiently large t. Furthermore, for each n, we study the final time at which fragments of size k^{-n} exist. In particular, by relating our branching random walk to a certain point process, we show that, after suitable rescaling, the laws of these times converge to a Gumbel distribution as n→∞.

Based on joint work with Piotr Dyszewski, Samuel G. G. Johnston, Joscha Prochno and Dominik Schmid

Paolo Dai Pra (Università degli Studi di Verona)

Self-sustained oscillations in interacting systems: an overview and some recent advances

Abstract: Self organized collective periodic behavior is seen to emerge in several different contexts: from neuroscience to tectonic plates movements, from population dynamics to epidemiology. A large variety of stochastic models have been proposed to capture this phenomenon at a mathematical level, showing that it may be induced by a combination of factors including noise, dissipation, loss of Markovianity and/or of time reversibility. Most of the present literature concerns mean-field models, where the thermodynamic limit is well understood at a dynamical level, and the emergence of oscillations can be seen from the macroscopic evolution equations. In models with short range interaction it is much harder to understand how self organization at microscopic level may produce large scale rhythms. Some partial results have been obtained for a non-reversible modification of the nearest neighbour Ising model.

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## Summer term 2021, online via Zoom

Friday, July 9, 2021, 4 pm (!) CET ct,  Rhein-Main-Kolloquium Stochastik, Johannes Gutenberg-Universität Mainz, online via Zoom

Please note that we will start one hour later than usual at 4 pm ct.

Pascal Maillard (Toulouse)
Markus Heydenreich (LMU München)

Programme (times are CET):

4.15 pm: Pascal Maillard (Toulouse): Branching particle systems and front propagation

Abstract: I will review some recent results (some in progress) on extremes of branching particle systems as models of front propagation. The main theme will be asymptotic results about speed and fluctuations. The talk will be based on joint work with various subsets of the following people : Gaël Raoul, Michel Pain, Sarah Penington, Jason Schweinsberg, Julie Tourniaire.

5.15 pm: Virtual coffee break (Gathertown link see below)

5.45 pm: Markus Heydenreich (LMU München): Voronoi cells in random split trees

Abstract: Consider a large graph G, and choose k vertices uniformly. We study the proportional size of the Voronoi cells of these k vertices as the number of vertices increases (but k kept fix). We identify the scaling of proportional sizes of the Voronoi cells for the case that G is a random split tree. Indeed, in this case, the largest of these k Voronoi cells contains most of the vertices, while the sizes of the remaining ones are of smaller order. This “winner-takes-all” phenomenon persists if we modify the definition of the Voronoi cells by introducing random edge lengths (with suitable moment assumptions), or assign different influence parameters (“speeds”) to each of the k vertices. We achieve this by investigating the typical shape of large random split trees.
Our findings are in contrast to corresponding results on random uniform trees and on the continuum random tree, where it is known that the vector of the relative sizes of the k Voronoi cells is asymptotically uniformly distributed on the (k − 1)-dimensional simplex.
Based on joint work with Cécile Mailler and Alexander Drewitz.

June 11, 2021, 15 c.t. CET, Rhein-Main-Kolloquium Stochastik,  Goethe-Universität Frankfurt/Main, online via Zoom

15:15-16:15: Gaultier Lambert (Universität Zürich)

16:15-16:45: virtual coffee break

16:45-17:45: Christian Brennecke (Harvard University)

Abstracts:

Gaultier Lambert (Zurich): Normal approximation for traces of random unitary matrices

This talk aim to report on the fluctuations of traces of powers of a random n by n matrix U distributed according to the Haar measure on the unitary group. This classical random matrix problem has been extensively studied using several different methods such as asymptotics of Toeplitz determinants, representation theory, loop equations etc. It turns out that for any k≥1, Tr[U^k] converges as n tends to infinity to a Gaussian random variable with a super exponential rate of convergence. In this talk, I will explain some of these results and present some recent work with Kurt Johansson (KTH) in which we revisited this problem in a multivariate setting.

Christian Brennecke (Harvard): On the TAP equations for the Sherrington-Kirkpatrick Model

In this talk, I will review the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass and present a dynamical derivation, valid at sufficiently high temperature. In our derivation, the TAP equations follow as a simple consequence of the decay of the two point correlation functions. The methods can also be used to establish decay of higher order correlation functions. We illustrate this by proving a suitable decay bound on the three point functions which implies an analogue of the TAP equations for the two point functions. The talk is based on joint work with A. Adhikari, P. von Soosten and H.T. Yau.

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### Online-Termine im Wintersemester 2020/21

Fr., 22.01.2021:

Siva Athreya (Bangalore) und Mia Deijfen (Stockholm)

Fr., 29.01.2021:

Gábor Lugosi (Pompeu Fabra University, Barcelona) und Po-Ling Loh (University of Wisconsin, Madison)

Fr., 12.02.2021:
Rongfeng Sun (Singapore) und Nikos Zygouras (Warwick)

### Termine im Wintersemester 2019/20

15.11.2019 - JGU Mainz:     Amandine Véber (Paris):

Resource sharing with logarithmic weights

Sarah Penington (Bath):

Branching Brownian motion with selection and a free boundary problem

06.12.2019 - GU Frankfurt:  Simone Warzel (München):

Quantum spin glasses: a mathematical challenge

Abstract:

The theory of classical mean-field spin glasses is a well-established and celebrated field within probability theory.
The addition of a constant perpendicular magnetic field introduces a non-commuting term into the energy of such spin glasses and hence
causes quantum effects. The main aim of this talk is to give an overview over some of the motivations for the study of quantum spin glasses. I will also review some first mathematical results in this field. Among them is a derivation of the key features of the thermal phase diagram of the simplest of all mean-field spin glasses, the quantum random energy model.

Matthias Erbar (Bonn):

A variational characterization of the Sine_ß point process:

Abstract:

The one-dimensional log gas in finite volume is a system of particles interacting via a repulsive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sine_ß process constructed by Valko and Virag. Leblé and Serfaty have established a large deviation principle for the microscopic configurations governed by a rate function which is the sum of a specific entropy and a renormalized interaction energy. Thus the typical microscopic behavior of the gas is described by the minimizers of this free energy functional, one of which is the Sine_ß process. We show that this is indeed the unique minimizer. Our argument is based on optimal transport of random point configurations and exploits strict displacement convexity in the free energy functional.
Joint work with Martin Huesmann and Thomas Leblé

Ort: Goethe-Universität Frankfurt, Campus Bockenheim, Raum 711 (groß),  Robert-Mayer-Str. 10, 7. Stock, Frankfurt am Main

31.01.2020 - TU Darmstadt: Sabine Jansen (München) und Dimitris Tsagkarogiannis (l’Aquila)

### Freitag, 3. Mai 2019, TU Darmstadt | Altes Hauptgebäude, S1 03 | Raum 23,

15:15 Uhr: Herbert Spohn (TU München und Uni Bonn)

Gibbs measures of the Toda chain and random matrix theory

16:15 – 16:45 Uhr:    Kaffee und Tee

16:45 Uhr: Lisa Hartung (Johannes Gutenberg-Universität Mainz):

The Ginibre characteristic polynomial and Gaussian Multiplicative Chaos

Im Anschluss gemeinsame Nachsitzung.

### Freitag, 24. Mai 2019, Goethe-Universität Frankfurt, Campus Bockenheim, Robert-Mayer-Straße 10, RAUM 711 groß, 7. OG, Frankfurt am Main

15:15 h Roland Bauerschmidt (University of Cambridge):

Dynamics of strongly correlated spin systems

16:15 – 16:45 Uhr:    Kaffee und Tee

16:45 h Prof. Dr. Chiranjib Mukherjee (Universität Münster):

Gaussian multiplicative chaos in the Wiener space

Roland Bauerschmidt: Dynamics of strongly correlated spin systems
I will discuss some results on the problem of understanding the long-time behaviour of Glauber and Kawasaki dynamics of spin systems in the regimes of strong correlations. This is joint work with Thierry Bodineau.

Chiranjib Mukherjee: Gaussian multiplicative chaos in the Wiener space
In the classical finite dimensional setting, a Gaussian multiplicative chaos (GMC) is obtained by tilting an ambient measure by the exponential of a centred Gaussian field indexed by a domain in the Euclidean space. In the two-dimensional setting and when the underlying field is "log-correlated", GMC measures share close connection to the 2D Liouville quantum gravity, which has seen a lot of revived interest in the recent years.
A natural question is to construct a GMC in the infinite dimensional setting, where techniques based on log-correlated fields in finite dimensions are no longer available. In the present context, we consider a GMC on the classical Wiener space, driven by a (mollified) Gaussian space-time white noise. In $d\geq 3$, in a previous work with A. Shamov and O. Zeitouni, we showed that the total mass of this GMC, which is directly connected to the (smoothened) Kardar-Parisi-Zhang equation in $d\geq 3$, converges for small noise intensity to a well-defined strictly positive random variable, while for larger intensity (i.e. for small temperature) it collapses to zero. We will report on joint work with Yannic Bröker (Münster) where we study the endpoint distribution of a Brownian path under the GMC measure and show that, for low temperature, the endpoint GMC distribution localizes in few spatial islands and produces asymptotically purely atomic states.

### Freitag, 14. Juni 2019, Johannes Gutenberg-Universität Mainz, Raum 03-428, Staudingerweg 9, 55128 Mainz

15:15 Uhr Sebastian Andres (University of Cambridge)

Local Limit Theorems for the Random Conductance Model

16:15 – 16:45 Uhr:    Kaffee und Tee

16:45 Uhr Martin Slowik (TU Berlin)

Random walks among random conductances as rough paths

Sebastian Andres (University of Cambridge): Local Limit Theorems for the Random Conductance Model

The random conductance model is a well-established model for a random walk in random environment. In recent years, quenched functional central limit theorems and quenched local limit theorems for such random walks have been intensively studied, and such results have meanwhile been established also in the case of general ergodic, degenerate environments only satisfying a moment condition.

In this talk we will review those results and also discuss an annealed local limit theorem in the case of time-dependent conductances which can be used to prove a scaling limit result for the space-time covariances in the Ginzburg-Landau $\nabla\varphi$ model. This result applies to convex potentials for which the second derivative may be unbounded.

This talk is based on a joint work with Peter Taylor (Cambridge).

Martin Slowik (TU Berlin): Random walks among random conductances as rough paths

The random conductances model is a class of random walks in a reversible random environment.  Depending on the assumptions on the law of the environment, invariance principles à la Donsker (in uniform topology) are fairly well understood for such random walks. However, if the random walk acts as a noise term in a differential equation, scaling limits in a finer topology (rough path topology) has to be established in order to understand the convergence properties of the solution. After reviewing the results and methods that has been used to prove annealed and quenched invariance principles, I will discuss an annealed invariance principle in the rough path topology.

Im Anschluss gemeinsame Nachsitzung.

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# Stochastic processes on evolving network

### Technische Universität Darmstadt | Karolinenplatz 5, 64289 Darmstadt | S101 Room A2 (@Audimax Building)

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### Freitag 16.11.2018, Universität Mainz, Institut für Mathematik, Hilbertraum (Raum 05-432), Staudingerweg 9, 55128 Mainz

15:15  Prof. Alexander Schnurr (Siegen): The fourth characteristic of a semimartingale

We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space R^d. By carefully distinguishing between two killing states, we are able to introduce a fourth semimartingale characteristic which generalizes the fourth part of the Levy quadruple. Using the probabilistic symbol, we analyze the close relationship between the generators of certain Markov processes with killing and their (now four) semimartingale characteristics.

16:45 Prof. Markus Bibinger (Marburg): Statistical analysis of path properties of volatility

In this talk, we review recent contributions on statistical theory to infer path properties of volatility. The interest is in the latent volatility of an Itô semimartingale, the latter being discretely observed over a fixed time horizon.

We consider tests to discriminate continuous paths from paths with volatility jumps. Both a local test for jumps at specified times and a global test for jumps over the whole observation interval are discussed.

We establish consistency and optimality properties under infill asymptotics, also for observations with additional additive noise.

Recently, there is high interest in the smoothness regularity of the volatility process as conflicting models are proposed in the literature.

To address this point, we consider inference on the Hurst exponent of fractional stochastic volatility processes. Even though the regularity of the volatility determines optimal spot volatility estimation methods, forecasting techniques and the volatility persistence, its identifiability is one of the few unsolved questions in high-frequency statistics. We discuss a first approach which can reveal if path properties are stable over time or changing. Eventually, we discuss some recent considerations and conjectures on this open question.

### Freitag, 07.12.2018, TU Darmstadt, Physik Institut S2|07 Raum 167, Hochschulstraße 6, 64289 Darmstadt

15:15 Jakob Björnberg (Universität Göteborg): Random permutations and the Heisenberg model

Abstract:We discuss models for random permutations which are closely linked to quantum spin systems from statistical physics.

The cycle structure of the random permutations is intimately connected with the correlation structure in the spin-system, and it is expected that this cycle structure converges to a distribution known as Poisson--Dirichlet, in the limit of large systems.  This problem is still open but we present some partial progress.

16:45 Dr. Piotr Miłoś (Universität Warschau):Phase transition for the interchange and quantum Heisenberg models on the Hamming graph

Abstract: In my talk I will present a family of random permutation models on the 2-dimensional Hamming graph H(2,n), containing the interchange process and the cycle-weighted interchange process with parameter θ>0. This family contains the random representation of the quantum Heisenberg ferromagnet. The main result is that in these models the cycle structure of permutations undergoes a phase transition -- when the number of transpositions defining the permutation is <cn^2, for small enough c>0, all cycles are microscopic, while for more than >Cn^2 transpositions, for large enough C>0, macroscopic cycles emerge with high probability. For the quantum Heisenberg ferromagnet on H(2,n) this implies that for low enough temperatures spontaneous magnetization occurs, while it is not the case for high temperatures. At the core of our approach is a novel application of the cyclic random walk, which might be of independent interest. By analyzing explorations of the cyclic random walk, we show that sufficiently long cycles of a random permutation are uniformly spread on the graph, which makes it possible to compare our models to the mean-field case, i.e., the interchange process on the complete graph, extending the approach used earlier by Schramm (joint work with Radosław Adamczak, Michał Kotowski).

### Freitag 25.01.2019, Universität Frankfurt,Goethe-Universität Frankfurt, Institut für Mathematik, Robert-Mayer-Str. 10, 60486 Frankfurt Raum 711 (groß), 7. Stock

15:15 Uhr: Antti Knowles (Universität Genf)
Eigenvalues and eigenvectors of supercritical Erdos-Renyi graphs

Abstract: I review some recent results on Erdos-Renyi graphs G(N,p) near and above the critical scale pN = log N, where the graph undergoes a connectivity crossover. For pN >> log N, the graph G(N,p) is with high probability connected, while for pN << log N it has with high probability isolated vertices. In the supercritical regime pN >> log N, the eigenvalues stick to the bulk spectrum, a local law holds down to optimal scales, and the eigenvectors are completely delocalized. All three statements are false in the subcritical regime pN << log N. Based on joint work with F. Benaych-Georges, C. Bordenave, Y. He, and M. Marcozzi.

16:15 Uhr: Kaffee und Tee

16:45 Uhr: Aernout van Enter (Universität Groningen)
One-sided versus two-sided stochastic descriptions

Abstract: Stochastic systems can be parametrised by time (like Markov chains), in which conditioning is one-sided(the past) or by one-dimensional space (like Markov fields), where conditioning is two-sided (right and left). I will discuss some examples, in particular generalising this to g-measures versus Gibbs measures, when the two descriptions are the same and when they are different. We show the role one-dimensional entropic repulsion plays in this setting. Joint work with R. Bissacot, E. Endo and A. Le Ny

### Termine im Sommersemester 2018

Freitag, 18.05.2018, TU Darmstadt, S1|05 Raum 24 (Maschinenhaus)

15:15 Friedrich Götze (Universität Bielefeld): Asymptotic Expansions in Entropic Limit Theorems

We discuss the convergence in classical (central) limit theorems measured in relative entropy based divergences. This includes Entropy, Fisher-Information as well as Renyi-Divergences. Analogues of these expansions of divergences relative to the Wigner law in non-commutative probability are discussed as well.

16:45 Michael Scheutzow (TU Berlin): Generalized couplings and ergodicity

The coupling method is a classical tool to establish uniqueness and stability of an invariant measure of a Markov process. In this talk we recall the concept of a generalized coupling and show how it can be used to prove ergodicity (including rates of convergence). The approach is particularly useful in the analysis of stochastic delay equations and some class of SPDEs. This is joint work with Alex Kulik (Kiev) and Oleg Butkovsky (Haifa/Berlin).

Freitag, 22.06.2018, Universität Frankfurt, Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711 groß

15:15 Louigi Addario-Berry (McGill University, Montreal): The front location for branching Brownian motion with decay of mass

Consider a standard branching Brownian motion whose particles have varying mass. At time t, if a total mass m of particles have distance less than one from a fixed particle x, then the mass of particle x decays at rate m. The total mass increases via branching events: on branching, a particle of mass m creates two identical mass-m particles.

One may define the front of this system as the point beyond which there is a total mass less than one (or beyond which the expected mass is less than one). This model possesses much less independence than standard BBM, and martingales are hard to come by. However, using careful tracking of particle trajectories and a PDE approximation to the particle system, we are able to prove an almost sure law of large numbers for the front speed. We also show that, almost surely, there are arbitrarily large times at which the front lags distance ~ c t^{1/3} behind the typical BBM front. At a high level, our argument for the latter may be described as a proof by contradiction combined with fine estimates on the probability Brownian motion stays in a narrow tube of varying width.

This is joint work with Sarah Penington and Julien Berestycki.

16: 45 Julien Berestycki (University of Oxford): The hydrodynamic limit of two variants of Branching Brownian motion

In this talk, I'll consider two variants of branching Brownian motion (BBM): with decay of mass (as in Louigi's talk) and with selection. In the BBM with selection, the number of particles is fixed at some number N and is kept constant by killing the leftmost particle at each branching event. Both models are motivated by considerations from ecology and evolutionary biology.

A particle system has a hydrodynamic limit when, as the number of particles tends to infinity, the behaviour of the system becomes well approximated by the solution of a partial differential equation. In this case I will show that the behaviour of the BBM with decay of mass is governed by the non-local version of the celebrated Fisker-KPP equation while the BBM with selection tends to the solution of a new free boundary problem also in the Fisher-KPP class that we study.

This is based on joint work with Louigi Addario-Berry and Sarah Penington on the one hand and Eric Brunet and Sarah Penington on the other.

Freitag 06.07.2018, Universität Mainz, Institut für Mathematik, Staudingerweg 9, Hilbertraum (Raum 05-432)

15:15 Daniel Valesin (Rijksuniversiteit Groningen): The asymmetric multitype contact process

We study a class of interacting particle systems known as the multitype contact process on Z^d. In this model, sites of Z^d can be either empty or occupied by an individual of one of two species. Individuals die with rate one and send descendants to neighboring sites with a rate that depends on their (the parent's) type. Births are not allowed at sites that are already occupied. We assume that one of the types has a birth rate that is larger than that of the other type, and larger than the critical value of the standard contact process. We prove that, if initially present, the stronger type has a positive probability of never going extinct. Conditionally on this event, it takes over a ball of radius growing linearly in time. We also completely characterize the set of stationary distributions of the process and prove a complete convergence theorem.

Joint work with Pedro L.B. Pantoja and Thomas Mountford.

16:45 Jan Swart (UTIA, Prag): The mean-field dual of systems with cooperative branching

In this talk we consider interacting particle systems where pairs of particles can give birth to new particles, and in addition particles die with a certain rate. We are interested in the random map that describes how the state at a given time depends on the initial state, for well-mixing populations in the limit that the size of the population is large. We will reveal an interesting link to Random Tree Processes

(RTPs) as studied by Aldous and Bandyopadhyay, which are a sort of Markov chains with a tree-like time parameter. In particular, we will discuss endogeny of RTPs related to systems with cooperative branching.

This is joint work with Tibor Mach (Prague) and Anja Sturm (Göttingen).

### Termine im Wintersemester 2017/2018

Freitag, 19.01.2018

15:15 Uhr: Steffen Dereich (Münster): Extended notions of local convergence for sequences of random graphs

16:45 Uhr: Peter Mörters (Köln): Metastability of the contact process on evolving scale-free networks

Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

Freitag, 26.01.2018

15:15 Uhr: Wolfgang König (WIAS / TU Berlin): The principal part of the spectrum of random Schrödinger operators in large boxes

16:45 Uhr: Götz Kersting (Frankfurt): Laws of large numbers for general Lambda-coalescents

Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 8, Hilbertraum (302)

Freitag, 09.02.2018

15:15 Elisabetta Candellero (University of Warwick): Coexistence of competing first-passage percolation on hyperbolic graphs

16:45 Francesco Caravenna (University of Milano-Bicocca): Pinning model, universality and rough paths

Gebäude S2|07, Hörsaal 167 (Physik), Hochschulstraße 6

### Termine im Sommersemester 2017

Freitag, 28.04.2017

15:15 Uhr: Leif Döring (Mannheim): Skorokhod Embedding Problem for Lévy Processes

16:45 Uhr: Leonid Mytnik (TECHNION Haifa): On the zero set of super-Brownian motion

Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

Freitag, 23.06.2017

15:15 Uhr: Carsten Jentsch (Universität Mannheim): Statistical inference on party positions from texts: statistical modeling, bootstrap and adjusting for time effects

16:45 Uhr: Claudia Kirch (Universität Magdeburg): Frequency domain likelihood approximations for time series bootstrapping and Bayesian nonparametrics

Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711 (groß), 7. Stock

Freitag, 07.07.2017

15:15 Uhr: Mikhail Lifshits (St. Petersburg): Energy saving approximation of random processes

16:45 Uhr: Vitali Wachtel (Augsburg): First-passage times over moving boundaries for random walks with non-identically distributed increments

Fachbereich Mathematik, Ehemaliges Maschinenhaus, Magdalenenstr. 12, Geb. S1|05, Raum 23

### Termine im Wintersemester 2016/2017

Freitag, 25.11.2016

15:15 Uhr: Alexandre Stauffer (University of Bath): Multi-particle diffusion limited aggregation

16:45 Uhr: Dirk Zeindler (Lancaster University): The order of large random permutations with cycle weights

Physik-Institut, Hochschulstr. 6, Gebäude S2|07, Raum 167

Freitag, 27.01.2017

15:15 Uhr: Yvan Velenik (Université de Genève): The global Markov property: a review (and some new results)

16:45 Uhr: Amine Asselah (Université Paris-Est Créteil): Capacity of the range of a random walk in four dimensions

Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711 (groß), 7. Stock

Freitag, 03.02.2017

15:15 Uhr: Mark Podolskij (Aarhus): High frequency functionals of semimartingales: probabilistic results and statistical applications

16:45 Uhr: Mathieu Rosenbaum (Ecole Polytechnique, Paris): Rough Heston model: Pricing, hedging and microstructural foundations

Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

### Termine im Sommersemester 2016

Freitag, 13.05.2016

15:15 Uhr: Renato Soares dos Santos (WIAS Berlin): Random walk on random walks

16:45 Uhr: Alexander Drewitz (Universität Köln): Random walk among a Poisson system of moving traps

Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

Freitag, 01.07.2016

15:15 Uhr: Matthias Reitzner (Universität Osnabrück): Poisson Hyperplane Tessellations

16:45 Uhr: Christoph Thäle (Universität Bochum): Random polytopes and the hyperplane conjecture

Magdalenenstr. 12, Gebäude S1 | 05 (Ehemaliges Maschinenhaus), Raum 22

Freitag, 15.07.2016

15:15 Uhr: Christian Bender (Universität des Saarlandes): A first order backward stochastic partial differential equation for swing option pricing

16:45 Uhr: Frank Riedel (Universität Bielefeld): Financial equilibria under Knightian uncertainty about volatility

Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711 (groß), 7. Stock

### Termine im Wintersemester 2015/2016

Freitag, 04.12.2015, 15 - 18 Uhr

15:15 Uhr: Olivier Garet (Université de Lorraine, Nancy): Essential hitting times for the contact process

16:45 Uhr: Régine Marchand (Université de Lorraine, Nancy): The number of open paths in supercritical oriented percolation

Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

Freitag, 22.01.2016

15:15 Uhr: Amin Coja-Oghlan (Universität Frankfurt): Limit of discrete distributions and Gibbs measures on random graphs

16:45 Uhr: Lutz Warnke (University of Cambridge): The phase transition in bounded-size Achlioptas processes

Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711 (groß), 7. Stock

Freitag, 05.02.2016

15:15 Uhr: René Schilling (TU Dresden): Level sets of Feller processes

16:45 Uhr: Jean Bertoin (Universität Zürich): Compensated Fragmentations

Ehemaliges Maschinenhaus, Magdalenenstr. 12 (Gebäude S1|05), Raum 23

### Termine im Sommersemester 2015

Freitag, 29.05.2015, 15 - 18 Uhr

15:15 Uhr: Vincent Vargas (Ecole Normale Supérieure, Paris): Liouville quantum gravity on the Riemann sphere (Part I)

16:45 Uhr: Rémy Rhodes (Université Paris-Est Marne La Vallée): Liouville quantum gravity on the Riemann sphere (Part II)
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711 (groß), 7. Stock

Freitag, 12.06.2015, 15 - 18 Uhr

15:15 Uhr: Paul Jenkins (University of Warwick): New evolutionary models for patterns of genetic variation along a DNA sequence

16:45 Uhr: Peter Pfaffelhuber (Universität Freiburg): Recombination as a tree-valued process along the genome
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

Freitag, 10.07.2015, 15 - 18 Uhr

15:15 Uhr: Loïc Chaumont (Université Angers): Time change in multitype branching processes with application to mutations

16:45 Uhr: Ron Doney (University of Manchester): A NASC for the strong renewal theorem via local large deviations
Magdalenenstr. 12 (Gebäude S1|05), Raum 22

### Termine im Wintersemester 2014/2015

Freitag, 05.12.2014, 15 - 18 Uhr

15:15 Uhr: Xue-Mei Li (University of Warwick): Stochastic homogeneization on Lie groups

16:45 Uhr: Martin Hairer (University of Warwick): Weak Universality of the KPZ equation
Fachbereich Mathematik, Hochschulstraße (Gebäude S2|04), Raum 213 (2. Stock)

Freitag, 23.01.2015, 15 - 18 Uhr

15:15 Uhr: Olivier Zindy (Paris 6): Poisson-Dirichlet statistics for the extremes of log-correlated Gaussian fields

16:45 Uhr: Louis-Pierre Arguin (Université de Montréal): Gaussian fields and the maxima of the Riemann Zeta function on the critical line
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

Freitag, 30.01.2015, 15 - 18 Uhr

15:15 Uhr: Zakhar Kabluchko (Münster): Asymptotic expansions for profiles of branching random walks and random trees

16:45 Uhr: Remi Monasson (CNRS/Ecole polytechnique): Statistical physics of the representation(s) of space in the brain
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

### Termine im Sommersemester 2014

Freitag, 23.05.2014, 15 - 18 Uhr

15:15 Uhr: Jiří Černý (Wien): Vacant set of random walk on discrete torus

16:45 Uhr: Noam Berger (TU München): Local CLT for ballistic random walk in random environment
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

Freitag, 06.06.2014, 15 - 18 Uhr

15:15 Uhr: Volker Betz (TU Darmstadt): Long cycles of spatial random permutations

16:45 Uhr: Steffen Dereich (Münster): Condensation in  preferential attachment models  with fitness
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

Freitag, 27.06.2014, 15 - 18 Uhr

15:00 Uhr: Markus Heydenreich (Leiden): Spontaneous breaking of rotational symmetry in the presence of defects

16:30 Uhr: Erwin Bolthausen (Zürich): Exit distributions for random walks
in anisotropic random environments

Fachbereich Mathematik, Schloßgartenstr. 7 (Gebäude S2|15), Raum 244 (2. Stock)

### Termine im Wintersemester 2013/2014

Freitag, 22.11.2013, 15 - 18 Uhr

15:15 Uhr: Martin Zerner (Tübingen): On the forward branching process for one-dimensional excited random walks

16:45 Uhr: Artem Sapozhnikov (Leipzig): Quenched invariance principle for simple random walk in correlated percolation models
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

Freitag, 13.12.2013, 13.30 - 16.30 Uhr

13:30 Uhr: Jean-François Marckert (Bordeaux): Compact convexes of the plane and probability theory

15:00 Uhr: Rudolf Grübel (Hannover): From trees to functions to ultrametric spaces, and back
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

Freitag, 31.01.2014, 15.30 - 18.30 Uhr

15:30 Uhr: Zhan Shi (Paris): Biased random walks on trees

17:00 Uhr: Anton Bovier (Bonn): Extremal processes in branching Brownian motions
Fachbereich Mathematik, Schloßgartenstr. 7 (Gebäude S2/15), Raum 51

### Termine im Sommersemester 2013

Freitag, 24.05.2013, 15 - 18 Uhr

15:15 Uhr: Jean-François Le Gall (Université Paris-Sud): The Brownian map: A universal model of random geometry

16:45 Uhr: Alison Etheridge (University of Oxford): Modelling natural selection
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

Freitag, 12.07.2013, 15 - 18 Uhr

15:15 Uhr: Francesco Caravenna (Mailand): Scaling limits and universality for random pinning models

16:45 Uhr: Dima Ioffe (Technion Haifa + Bonn): An invariance principle for random walks with prewetting
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

### Termine im Wintersemester 2012/2013

Freitag, 23.11.2012, 15 - 18 Uhr

15:15 Uhr: Igor Kortchemski (Université Paris 11): Galton-Watson trees conditioned to be large

16:45 Uhr: Patrick Hoscheit (CERMICS): Record processes on the continum random tree
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 8, Raum 302 (Hilbertraum), 3. Stock

Freitag, 01.02.2013, 15 - 18 Uhr

15:15 Uhr: Barbara Gentz (Bielefeld): The effect of noise on mixed-mode oscillation

16:45 Uhr: Nils Berglund (Orléans): Quantifying neuronal spiking patterns using continuous-space Markov chains
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

### Termine im Sommersemester 2012

Donnerstag, 28.06.2012, 16 - 19 Uhr

16:00 Uhr: Thomas G. Kurtz (University of Wisconsin -
Madison): Particle representations and limit theorems for stochastic
partial differential equations

17:30 Uhr: Steven N. Evans (University of California at Berkeley): Uplift under Lévystan: Lipschitz minorants of Lévy processes
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

### Termine im Wintersemester 2011/2012

Freitag, 25.11.2011, 15 - 18 Uhr

15:15 Uhr: Marie Albenque (École Polytechnique, derzeit TU Berlin): Convergence of stack-triangulations

16:45 Uhr: Nicolas Broutin (INRIA Rocquencourt): Cutting down trees, and putting them back togehter
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

Freitag, 10.02.2012, 15 - 18 Uhr

15:15 Uhr: Patrik Ferrari (Bonn): Interacting particle systems and random matrices

16:45 Uhr: Neil O'Connell (Warwick): Exactly solvable random polymers and their continuum scaling limits
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

### Termine im Sommersemester 2011

Freitag, 13.05.2011, 15 - 19 Uhr

15:00 Uhr: Nathanael Berestycki (Cambridge): Asymptotic behaviour of near-critical branching Brownian motion

16:15 Uhr: Henri Berestycki (Paris): Generalized principal eigenvalues of elliptic operators in unbounded domains and applications

17:15 Uhr: Julien Beresticki (Paris): Branching Brownian motion seen from its tip
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

Freitag, 10.06.2011, 15 - 18 Uhr

15:15 Uhr: Francis Comets (Paris): KPP equation in a space-time random medium

16:45 Uhr: Nina Gantert (München): Einstein relation for reversible motions in random medium
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

### Termine im Wintersemester 2010/2011

Freitag, 21.01.2011, 15 - 18 Uhr

15:15 Uhr: Amandine Véber (Paris): Spatial Lambda-Fleming-Viot process : genealogies in the presence of recombination

16:45 Uhr: Peter Mörters (Bath): Typical distances in ultrasmall random networks
Universität Frankfurt
Institut für Mathematik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

Freitag, 04.02.2011, 15 - 18 Uhr

15:15 Uhr: Markus Reiß (Berlin): Volatility estimation under microstructure noise and Le Cam theory

16:45 Uhr: Arnak Dalalyan (Paris): Aggregation of Estimators
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

### Termine im Sommersemester 2010

Freitag, 23.04.2010, 15 - 18 Uhr

15.00 Uhr: Jan Swart (UTIA Prague): Intertwining of Markov processes and the contact process on the hierarchical group

16.45 Uhr: Silke Rolles (TU München): Bayesian analysis for reversible Markov chains
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

Freitag, 02.07.2010, 15 - 18 Uhr

15.15 Uhr: Andrej Depperschmidt (Freiburg): Modelling protein translocation: A Brownian ratchet

16.45 Uhr: Frank den Hollander (Leiden University, EURANDOM): Random Walk in Dynamic Random Environment
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 432 (Hilbertraum), 5. Stock

### Termine im Wintersemester 2009/2010

Freitag, 15.01.2010, 15 - 18 Uhr

15.15 Uhr: Anja Sturm
(Göttingen): Koexistenz und Konvergenz für Wählermodelle mit Selektion.

16.45 Uhr: Jochen Blath (TU Berlin): The Symbiotic Branching Model: Moment Spectrum, Longtime-behaviour and Width of the Interface.
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-136

Freitag, 12.02.2010, 15 - 18 Uhr
15.15 Uhr: Dirk Metzler (LMU München): Efficient parameter estimation in population genetic models of complex demography.

16.45 Uhr: Jean-François Delmas (École des Ponts, Paris und Marne-la-Vallée): Most recent common ancestor and bottleneck in a simple size-varying population model.
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

### Termine im Wintersemester 2007/2008

Mittwoch, 28.11.2007, 15 - 18 Uhr
15.15 Uhr: Robert Griffiths (Oxford): Diffusion processes and coalescent trees.

16.45 Uhr: Matthias Birkner (WIAS Berlin): Towards a mathematical population genetics with highly skewed offspring distributions.
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

Mittwoch, 19.12.2007, 15 - 18 Uhr
15.15 Uhr: Susanne Ditlevsen (Kopenhagen): Parameters of stochastic diffusion processes estimated from observations of first hitting-times.

16.45 Uhr: Gaby Schneider (Frankfurt): Messages of oscillatory correlograms - a spike-train model.
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

Mittwoch, 16.01.2008, 15 - 18 Uhr
15.15 Uhr: Remco van der Hofstad (TU Eindhoven): Universality of distances in power-law random graphs.

16.45 Uhr: Mihyun Kang (HU Berlin): Evolution, phase transition and giant component of random graphs.
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 711, 7. Stock

### Termine im Sommersemester 2007

Mittwoch, 02.05.2007, 15 - 18 Uhr
'Random Graphs and their Random Limits'

15.15 Uhr: Matthias Winkel (Oxford): Convergence of discrete random trees: some theory and applications.

16.45 Uhr: Rongfeng Sun (Berlin): The Brownian net.
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

Mittwoch, 06.06.2007, 15 - 18 Uhr
'Stochastics in Neuro Sciences'

15.15 Uhr: Nihat Ay
(Leipzig): Relating stochastic dependence to information flows.

16.45 Uhr: Jochen Triesch (Frankfurt): How do different forms of neuronal plasticity interact?
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

Freitag, 06.07.2007
'Math Finance'

16.15 Uhr: Claudia Klüppelberg (TU München): On a Lévy-driven continuous time GARCH model.

17.45 Uhr: Hanspeter Schmidli (Universität Köln): Optimisation problems in non-life insurance.
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

### Termine im Sommersemester 2006

Mittwoch, 21.06.2006, 15 - 18 Uhr
15.15 Uhr: Christina Goldschmidt (Cambridge): Random recursive trees and the Bolthausen-Sznitman coalescent.

16.45 Uhr: Alois Panholzer (Wien): Applications of generating functions for limiting distribution results in random tree models.
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

Mittwoch, 05.07.2006
17:00 Uhr: P. Lánský (Institute of Physiology, Czech Academy of Sciences): Simple stochastic neuronal models and problems beyond frequency coding.
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

### Termine im Wintersemester 2005/2006

Mittwoch, 25.01.2006, 15 - 18 Uhr
15.15 Uhr: Amaury Lambert (Paris VI): The logistic branching process, coalescence with fragmentation, and fixation of mutant alleles.

17:00 Uhr: Brigitte Chauvin (Versailles): Connecting the random bisection problem and the binary search trees.
Universität Frankfurt
Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

Mittwoch, 15.02.2006, 15 - 18 Uhr
15.15 Uhr: Werner Kilb
(Physiologie Mainz): Dynamische Veränderungen im Membranpotential: vom Ionenkanal zum Netzwerk.

17:00 Uhr: Reinhard Höpfner (Mainz): Ein Datensatz von Membranpotentialen.
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

### Termine im Sommersemester 2005

Mittwoch, 27.04.2005, 15 - 18 Uhr
Doktorandenkolloquium

R. Alkemper (Mainz): Reskalierung von Voter-Modellen.

M. Hutzenthaler (Frankfurt): Ergodisches Verhalten von verzweigenden Populationen mit lokaler Konkurrenz.
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

Mittwoch, 11.05.2005, 15 - 18 Uhr
Doktorandenkolloquium

N. Gerresheim
(Mainz): Stark rekurrente katalytisch verzweigende Irrfahrten auf der hierarchischen Gruppe.

T. Ali Khan (Frankfurt): Stochastic analysis of algorithms and game trees.
Universität Frankfurt
FB Mathematik, Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

Mittwoch, 25.05.2005, 15 - 18 Uhr
'Neuronen'

H. Luhmann (Mainz): Das Neuron: ein plastischer analog-digital Wandler.

S. Grün (FU Berlin): Detektion und Identifikation neuronaler Wechselwirkung im kortikalen Netzwerk.
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 05-432 (Hilbertraum)

Mittwoch, 08.06.2005, 15 - 18 Uhr
'Coalescents'

M. Möhle (Tübingen): Coalescent Theory - Simultaneous Multiple Collisions and Sampling.

J. Bertoin (Paris VI): Some aspects of random fragmentations.
Universität Mainz
Institut für Mathematik, Staudingerweg 9, Raum 04-422

Mittwoch, 22.06.2005, 15 - 18 Uhr
'Finanzmathematik'

J. Cerny
(WIAS Berlin): The stock price evolution from microscopic market modelling.

J. Kallsen (TU München): On the structure of general mean-variance hedging strategies.
Universität Frankfurt
FB Mathematik, Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

Mittwoch, 20.07.2005, 15 - 18 Uhr
'Stochastische Algorithmen'

J. Blömer
(Paderborn): Kryptografie auf Smartcards - Seitenangriffe und Sicherheit durch Randomisierung.

M. Dietzfelbinger (Ilmenau): Daten zufällig verteilen - und dann schnell wieder finden: Neuere Hashverfahren.
Universität Frankfurt
FB Mathematik, Institut für Stochastik und Mathematische Informatik, Robert-Mayer-Str. 10, Raum 110, 1. Stock

Last update: 27.11.2017, S. Grün, gruen@mathematik.uni-mainz.de