Random Matrix & Probability Theory Seminar

Beginning immediately, until at least December 31, all seminars will take place virtually, through Zoom.

In the 2020-2021 AY, the Random Matrix and Probability Theory Seminar will take place on select Wednesdays from 2:00 – 3:00pm virtually. This seminar is organized by Christian Brennecke (brennecke@math.harvard.edu ) and Per von Soosten (vonsoosten@math.harvard.edu).

To learn how to attend this seminar, please fill out this form.

The schedule below will be updated as the details are confirmed.

9/9/2020Yukun He (Zurich)Title: Single eigenvalue fluctuations of sparse Erdős–Rényi graphs

Abstract: I discuss the fluctuations of individual eigenvalues of the adjacency matrix of the Erdös-Rényi graph $G(N,p)$. I show that if $N^{-1}\ll p \ll N^{-2/3}, then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. The main technical tool of the proof is a rigidity bound of accuracy $N^{-1-\varepsilon}p^{-1/2}$ for the extreme eigenvalues, which avoids the $(Np)^{-1}$-expansions from previous works. Joint work with Antti Knowles.
10/14/2020David Belius (University of Basel)Title: The TAP approach to mean field spin glasses

Abstract: The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirkpatrick mean field spin glass model was proposed in one of the earliest papers on this model. Since then it has complemented subsequently elaborated methods  in theoretical physics and mathematics, such as the replica method, which are largely orthogonal to the TAP approach. The TAP approach has the advantage of being interpretable as a variational principle optimizing an energy/entropy trade-off, as commonly encountered in statistical physics and large deviations theory, and potentially allowing for a more direct characterization of the Gibbs measure and its “pure states”. In this talk I will recall the TAP approach, and present preliminary steps towards a solution of mean field spin glass models entirely within a TAP framework.
10/28/2020Giuseppe Genovese (University of Basel)TitleNon-convex variational principles for the RS free energy of restricted Boltzmann machines

Abstract: From the viewpoint of spin glass theory, restricted Boltzmann machines represent a veritable challenge, as to the lack of convexity prevents us to use Guerra’s bounds. Therefore even the replica symmetric approximation for the free energy presents some challenges. I will present old and new results around the topic along with some open problems. 
3:00 – 4:00pm
Lucas Benigni (University of Chicago)TBA
11/18/2020Simone Warzel (Technical University of Munich)TBA
12/2/2020Sabine Jansen (LMU Munich)TBA

For information on previous seminars, click here

The schedule will be updated as details are confirmed.

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