Upper-tail large deviation principle for the ASEP

TL;DR

This paper derives the exact large deviation rate function for the integrated current in ASEP, revealing its asymptotic behavior and connecting it with known results for TASEP, thus advancing understanding of exclusion processes.

Contribution

It provides the explicit Lyapunov exponents and the upper-tail large deviation rate function for ASEP, extending previous TASEP results to the asymmetric case.

Findings

Exact Lyapunov exponents for ASEP current

Explicit upper-tail large deviation rate function

Matching results with TASEP rate function

Abstract

We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ started from step initial data and obtain the exact Lyapunov exponents for $H_0(t)$, the integrated current of ASEP. As a corollary, we derive an explicit formula for the upper-tail large deviation rate function for $-H_0(t)$. Our result matches with the rate function for the integrated current of the totally asymmetric simple exclusion process (TASEP) obtained in [Johansson 00](arXiv:math/9903134).