One-point asymptotics for half-flat ASEP

TL;DR

This paper rigorously derives the asymptotic behavior of the ASEP height function with half-flat initial condition, showing it converges to the Airy_{2→1} process, confirming a prior conjecture through exact formula analysis.

Contribution

It provides a rigorous derivation and asymptotic analysis of the ASEP height function's distribution, confirming the conjectured connection to the Airy_{2→1} process.

Findings

ASEP height function converges to Airy_{2→1} process

Rigorous derivation of asymptotics for half-flat ASEP

Validation of prior conjecture on process limit

Abstract

We consider the asymmetric simple exclusion process (ASEP) with half-flat initial condition. We show that the one-point marginals of the ASEP height function are described by those of the $\mbox{Airy}_{2 \rightarrow 1}$ process, introduced by Borodin-Ferrari-Sasamoto in (Commun. Pure Appl. Math., 61, 1603-1629, 2008). This result was conjectured by Ortmann-Quastel-Remenik (Ann. Appl. Probab., 26, 507-548), based on an informal asymptotic analysis of exact formulas for generating functions of the half-flat ASEP height function at one spatial point. Our present work provides a fully rigorous derivation and asymptotic analysis of the same generating functions, under certain parameter restrictions of the model.