ASEP via Mallows coloring

TL;DR

This paper investigates the asymptotic behavior of ASEP with finitely many particles under a specific randomized initial condition, revealing its KPZ limit behavior and introducing a novel Mallows permutation coloring technique.

Contribution

It introduces a new coloring method for ASEP particles using Mallows permutations and analyzes the process's KPZ limit behavior under certain initial conditions.

Findings

ASEP with finitely many particles exhibits KPZ limit behavior.

A new Mallows permutation-based coloring technique for ASEP particles.

The randomized initial condition is optimal for asymptotic analysis.

Abstract

In this paper we study the asymptotic behavior of the Asymmetric Simple Exclusion Process (=ASEP) with finitely many particles. It turns out that a certain randomized initial condition is the most amenable to such an analysis. Our main result is the behavior of such an ASEP in the KPZ limit regime. A key technical tool introduced in the paper -- the coloring of ASEP particles with the use of random Mallows permutations -- may be of independent interest.