Joint distribution of currents in the symmetric exclusion process

TL;DR

This paper characterizes the joint statistical properties and correlations of currents and particle densities in the symmetric exclusion process, extending previous work on individual current distributions to a comprehensive multivariate analysis.

Contribution

It introduces a framework for analyzing the joint distribution of multiple currents and their correlations with particle density in the SEP, generalizing previous single-observable results.

Findings

Derived closed integral equations for current correlations.

Established boundary conditions with simple physical interpretations.

Quantified correlations between tracer displacement and particle current.

Abstract

The symmetric simple exclusion process (SEP) is a paradigmatic model of diffusion in a single-file geometry, in which the particles cannot cross. In this model, the study of currents have attracted a lot of attention. In particular, the distribution of the integrated current through the origin, and more recently, of the integrated current through a moving reference point, have been obtained in the long time limit. This latter observable is particularly interesting, as it allows to obtain the distribution of the position of a tracer particle. However, up to now, these different observables have been considered independently. Here, we characterise the joint statistical properties of these currents, and their correlations with the density of particles. We show that the correlations satisfy closed integral equations, which generalise the ones obtained recently for a single observable. We also obtain boundary conditions verified by these correlations, which take a simple physical form for any single-file system. As a consequence of our results, we quantify the correlations between the displacement of a tracer, and the integrated current of particles through the origin.