# Mathematical Sciences Research Institute

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# Seminar

Program Associate Short Talks (3x 25 mins) October 11, 2021 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Sayan Das (Columbia University), Kevin Yang (Stanford University), Weitao Zhu (Columbia University)
Description No Description
Video

#### PA Talk- Weitao Zhu

Abstract/Media

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1:30 - 1:55: Sayan Das

Title: Large Deviations for Discrete Beta-Ensembles

Abstract: Discrete beta-ensembles are stochastic N-particle ensembles that are integrable discretizations for general beta log-gases of random matrix theory. Introduced by Borodin, Gorin, and Guionnet, these ensembles have connections to discrete Selberg integrals and several models in integrable probability including uniform random tilings, (z;w)-measures, and Jack measures. In this talk, under general assumptions on the potential, we establish a large deviation principle for the rightmost particle of these measures. Based on joint work with Evgeni Dimitrov.

2:00 - 2:25: Kevin Yang

Title: KPZ and Boltzmann-Gibbs Principle

Abstract: The KPZ equation is a canonical model for random interfaces, though for interfaces associated to interacting particle systems, rigorous proof of universality has been limited to only a handful of special models. We will discuss recent progress for a general class of models that is based on a new non-stationary Boltzmann-Gibbs Principle. We also discuss applications of this Boltzmann-Gibbs principle beyond KPZ as well as possible improvements and extensions.

2:30 - 2:55: Weitao Zhu

Title: Upper-Tail Large Deviation Principle of the ASEP

Abstract: In this talk, we study the asymmetric simple exclusion process (ASEP) on $\Z$ started from step initial data. In particular, we discuss the Lyapunov exponent associated with the ASEP's height function $H_0(t)$ and derive its lower-tail large deviation rate function accordingly as the Legendre-Fenchel dual of the Lyapunov exponent. The talk is based on joint work with Sayan Das.

 KPZ and Boltzmann-Gibbs Principle 339 KB application/pdf Large Deviations for Discrete Beta-Ensembles 395 KB application/pdf Upper-Tail Large Deviation Principle of the ASEP 418 KB application/pdf