A limit theorem for particle current in the symmetric exclusion process

TL;DR

This paper establishes a general limit theorem for the particle current in the symmetric exclusion process, demonstrating Gaussian convergence under broad conditions without requiring translation invariance or specific initial states.

Contribution

It introduces a new limit theorem for particle current in the symmetric exclusion process that applies to diverse initial configurations without assuming translation invariance.

Findings

Normalized current converges to Gaussian distribution

Results hold for most initial configurations

No translation invariance assumption needed

Abstract

Using the recently discovered strong negative dependence properties of the symmetric exclusion process, we derive general conditions for when the normalized current of particles between regions converges to the Gaussian distribution. The main novelty is that the results do not assume any translation invariance, and hold for most initial configurations.