Distributional Limits for the Symmetric Exclusion Process

TL;DR

This paper explores the symmetric exclusion process, demonstrating how recent negative dependence results lead to convergence of certain functionals to Poisson and normal distributions, enhancing understanding of its probabilistic behavior.

Contribution

It applies recent negative dependence results to establish distributional convergence for functionals of the symmetric exclusion process.

Findings

Convergence to Poisson distribution for specific functionals.

Convergence to normal distribution for other functionals.

Enhanced understanding of the probabilistic limits of the process.

Abstract

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.