Dynamical Loop Equations

August 25, 2021
  • 60B20
  • 15B52
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.