Large Deviation Function of the Partially Asymmetric Exclusion Process

TL;DR

This paper extends the large deviation function analysis from the totally asymmetric exclusion process to the partially asymmetric case, revealing how asymmetry affects the scaling and finite-size corrections.

Contribution

It generalizes the large deviation function to the partially asymmetric exclusion process and derives finite-size corrections in the scaling limit.

Findings

Asymmetry rescales the scaling variable simply.

Finite-size corrections to the universal scaling function are obtained.

Universal cumulant ratio corrections are derived.

Abstract

The large deviation function obtained recently by Derrida and Lebowitz for the totally asymmetric exclusion process is generalized to the partially asymmetric case in the scaling limit. The asymmetry parameter rescales the scaling variable in a simple way. The finite-size corrections to the universal scaling function and the universal cumulant ratio are also obtained to the leading order.