Freitag, 11.06.2021: ONLINE-Veranstaltung

Zoom access to the talks:

https://uni-frankfurt.zoom.us/j/94648348387?pwd=anVJNnJKY2NZTVBGZWR4UXdGRHpOUT09

Meeting ID: 946 4834 8387

Passcode: 969450

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

16:15-16:45: virtual coffee break

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

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Gaultier Lambert: 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: 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.