The Asymmetric Simple Exclusion Process: October 2-6, 2023

Organized By:

  • Ivan Corwin, Columbia University
  • Evita Nestoridi, Stony Brook University
  • Dominik Schmid, University of Bonn

The asymmetric simple exclusion process (ASEP) is a central model in research on integrable probability and interacting particle systems. It is one of the most prominent examples of a stochastic interface growth model, which gives under a suitable weakly scaling rise to a solution of the KPZ equation; see surveys by Corwin [10, 11], and the seminal work [17] by Kardar, Parisi and Zhang for an overview. Other integrable models with similar properties include the stochastic six vertex model, log-gamma and O’Connell-Yor polymers. The particular case of the open ASEP is defined as the following interacting particle system. Particles occupy sites in a finite segment {1, …, N}for some N ∈ N, and they jump left at rate q and right at rate 1. Moreover, particles are inserted into site 1 at rate α and removed from there at rate γ, while at site N insertion occurs at rate δ and removal at rate β. All moves that violate the rule of at most one particle per site at a given time are excluded. In recent years, various breakthroughs in the study of asymmetric exclusion processes could be achieved.