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Seminar

Program Associate Short Talks September 13, 2021 (01:30 PM PDT - 03:00 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Yujin Kim (New York University, Courant Institute), Guido Mazzuca (International School for Advanced Studies (SISSA/ISAS)), Daniel Ofner (The Hebrew University of Jerusalem)
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Program Associate Short Talks

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To participate in this seminar, please register HERE.

This seminar is complied of three 25 minute talks. The order of speakers is as follows:

Speaker 1: Yujin Kim

Title: The Extreme of Branching Brownian Motion in R^d

Abstract: The extremal processes of Branching Brownian motion (BBM) have greatly informed the study of many other log-correlated fields. In dimension 1, the extremal processes of BBM have been studied extensively: of note is the convergence of the re-centered maximum (Bramson, 1983), and the description of the limiting extremal point process (Aidekon et. al./Arguin et. al., 2011). In this talk, we discuss recent work on BBM in dimensions two and higher proving that the maximum modulus converges in distribution to a randomly shifted Gumbel after re-centering. Time permitting, we will also discuss forthcoming results on the limiting extremal point process. Based on joint works with Julien Berestycki, Eyal Lubetzky, Bastien Mallein, and Ofer Zeitouni.

Speaker 2: Daniel Ofner

Title: Mesoscopic Universality for Orthogonal Polynomial Ensembles on the Unit Circle

Abstract: Orthogonal polynomial ensembles (OPE) on the unit circle are a certain class of point processes that arise naturally in random matrix theory and statistical mechanics. One special case of such a process is the extensively studied Circular Unitary Ensemble. In this talk we discuss the connection between OPE's and orthogonal polynomials on the unit circle. In particular, we show that in order to study asymptotics of the mesoscopic fluctuations of the empirical measure it is sufficient to understand the asymptotics of the associated recurrence coefficients. This is joint work with J. Breuer.

Speaker 3: Guido Mazzuca

Title: Alpha Ensembles and Integrable Systems

Abstract: In my talk I will introduce some tridiagonal random matrix models related to the classical beta ensembles in the high temperature regime, i.e. when the size N of the matrix tends to infinity with the constraint that βN=2α constant, α>0. I will show how to explicitly compute the mean density of states and the mean spectral measure for this ensemble. Finally, I will apply these results to compute the mean density of states for the periodic Toda lattice in thermal equilibrium. This talk is mainly based on • G.M., “On the mean Density of States of some matrices related to the beta ensembles and an application to the Toda lattice”, arXiv preprint:2008.04604, • G. M., and P.J. Forrester “The classical beta ensembles with beta proportional to 1/N: from loop equations to Dyson's disordered chain”. Journal of Mathematical Physics 62, 073505 (2021). DOI: 10.1063/5.0048481 • T. Grava, A. Maspero, G. M., and A. Ponno: Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit. Communications in Mathematical Physics, 380 (2020), pp. 811–851. DOI: 10.1007/s00220-020-03866-2.

91478?type=thumb Guido Mazzuca 434 KB application/pdf
91479?type=thumb Yujin Kim 2.3 MB application/pdf

Program Associate Short Talks