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Dynamical Loop Equations

[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1 August 23, 2021 - August 27, 2021

August 25, 2021 (10:45 AM PDT - 11:45 AM PDT)
Speaker(s): Jiaoyang Huang (New York University, Courant Institute)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Dynamical Loop Equations
Abstract

Loop (or Dyson-Schwinger) equation is an important tool to study the global fluctuations of one dimensional log-gas type interacting particle systems. In this talk I will present a dynamical version of loop equations for large families of two dimensional interacting particle systems. Some examples include Dyson’s Brownian motion, Nonintersecting Bernoulli/Poisson random walks, corner process, measures on Gelfand-Tsetlin patterns and Macdonald process. Then I will explain how to use dynamical loop equations to understand global fluctuations of these systems. This is a joint work with Vadim Gorin.
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Dynamical Loop Equations

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