Fluctuations and skewness of the current in the partially asymmetric exclusion process

TL;DR

This paper uses Bethe Ansatz equations to compute current cumulants in the partially asymmetric exclusion process, providing explicit formulas for the first three cumulants and exploring their behavior in different asymmetry regimes.

Contribution

It introduces a finite size formula for the third cumulant of the current and analyzes its behavior under different asymmetry scalings, extending previous results.

Findings

Recovered known formulas for the first two cumulants

Derived an explicit finite size formula for the third cumulant

Obtained a simple integral form for the third cumulant in a specific asymmetry limit

Abstract

We use functional Bethe Ansatz equations to calculate the cumulants of the total current in the partially asymmetric exclusion process. We recover known formulas for the first two cumulants (mean value of the current and diffusion constant) and obtain an explicit finite size formula for the third cumulant. The expression for the third cumulant takes a simple integral form in the limit where the asymmetry scales as the inverse of the square root of the size of the system, which corresponds to a natural separation between weak and strong asymmetry.