Limit profiles of ASEP

TL;DR

This paper investigates the mixing times and cutoff profiles of the asymmetric simple exclusion process (ASEP) on segments, providing probabilistic results for various initial conditions without relying on algebraic methods.

Contribution

It introduces a general probabilistic framework to determine cutoff windows and profiles for ASEP based on KPZ limit theorems, applicable to multiple initial configurations.

Findings

Derived cutoff profiles for flat, half-flat, and step initial data.

Established probabilistic methods for ASEP analysis without algebraic tools.

Connected ASEP cutoff phenomena to KPZ universality class results.

Abstract

We study the asymmetric simple exclusion process (ASEP) on a segment $\{1,\ldots,b_N\}$ and are interested in its total variation distance to equilibrium when started from an initial configuration $\xi^{N}$. We provide a general result which gives the cutoff window and profile whenever a KPZ-type limit theorem is available for an extension of $\xi^{N}$ to $\mathbb{Z}$. We apply this result to obtain the cutoff window and profile of ASEP on the segment with flat, half-flat and step initial data. Our arguments are entirely probabilistic and make no use of Hecke algebras.