Rhein-Main Kolloquium Stochastik



Shared colloquium of the probability and statistics workgroups

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


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.

Access to links to the talks and coffee break is available at: stochastik@uni-mainz.de




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)


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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