Large deviations for the current and tagged particle in 1D nearest-neighbor symmetric simple exclusion

TL;DR

This paper establishes large deviation principles for the current and tagged particle in a 1D symmetric simple exclusion process, revealing different growth behaviors of the rate functions near and far from their zeroes.

Contribution

It provides the first large deviation principles and explicit rate functions for the current and tagged particle in 1D symmetric exclusion, extending previous law of large numbers results.

Findings

Large deviation principles are proved for the current and tagged particle.

Explicit rate functions are evaluated and analyzed.

Different growth behaviors of rate functions near and far from zero are identified.

Abstract

Laws of large numbers, starting from certain nonequilibrium measures, have been shown for the integrated current across a bond, and a tagged particle in one-dimensional symmetric nearest-neighbor simple exclusion [Ann. Inst. Henri Poincare Probab. Stat. 42 (2006) 567-577]. In this article, we prove corresponding large deviation principles and evaluate the rate functions, showing different growth behaviors near and far from their zeroes which connect with results in [J. Stat. Phys. 136 (2009) 1-15].