Limits of Multilevel TASEP and similar processes

TL;DR

This paper investigates the asymptotic behavior of multilevel TASEP-like stochastic processes on interlacing particle configurations, establishing a universal Brownian motion limit for these complex dynamics.

Contribution

It introduces a universal scaling limit for a broad class of interlacing particle dynamics, including multi-layer TASEP and domino tiling shuffling algorithms.

Findings

Reflected interlacing Brownian motions serve as a universal limit.

The results unify various models under a common asymptotic framework.

Provides rigorous proof of convergence for these stochastic processes.

Abstract

We study the asymptotic behavior of a class of stochastic dynamics on interlacing particle configurations (also known as Gelfand-Tsetlin patterns). Examples of such dynamics include, in particular, a multi-layer extension of TASEP and particle dynamics related to the shuffling algorithm for domino tilings of the Aztec diamond. We prove that the process of reflected interlacing Brownian motions introduced by Warren in \cite{W} serves as a universal scaling limit for such dynamics.