A combinatorial solution for the current fluctuations in the exclusion process

Abstract

We conjecture an exact expression for the large deviation function of the stationary state current in the partially asymmetric exclusion process with periodic boundary conditions. This expression is checked for small systems using functional Bethe Ansatz. It generalizes a previous result by Derrida and Lebowitz for the totally asymmetric exclusion process, and gives the known values for the three first cumulants of the current in the partially asymmetric model. Our result is written in terms of tree structures and provides a new example of a link between integrable models and combinatorics.