# TU Darmstadt / Goethe-Universität Frankfurt / Gutenberg-Universität Mainz

## Termine im Sommersemester 2019

### 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.

Kurze Wegbeschreibung:

Haupteingangstreppe (Hochschulstraße 1) S1 03  eintreten,

dann auf der gleichen Ebene geradeaus bis zum Ende des Flures (Gebäudekomplexes),

zum Hörsaal Nr. 23, gehen.

### 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.

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### 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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### Wegbeschreibungen

zur Anreise an die Uni Mainz finden Sie unter https://www.mathematik.uni-mainz.de/anfahrt/,

zur Anreise an die Uni Frankfurt unter https://www.uni-frankfurt.de/38074653/campus_bockenheim und https://www.uni-frankfurt.de/38093742/Campus_Bockenheim-pdf.pdf,