Rhein-Main Kolloquium Stochastik

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Shared colloquium of the probability and statistics workgroups

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

 

Summer term 2021, online via Zoom

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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Friday, July 9, 2021, 15 c.t. CET,  Rhein-Main-Kolloquium Stochastik, Johannes Gutenberg-Universität Mainz, online via Zoom

Pascal Maillard (Toulouse)
Markus Heydenreich (LMU München)

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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,

zur Anreise an die TU Darmstadt unter http://www3.mathematik.tu-darmstadt.de/fb/mathe/wir-ueber-uns/adresse-und-lageplan/anreise.html

Termine in früheren Semestern finden Sie hier.

stochastik@uni-mainz.de