On the correlations of some microscopic random systems

TL;DR

This paper studies the two-point correlation functions in boundary-driven interacting particle systems, showing they evolve according to PDEs linked to two-dimensional random walks, leading to asymptotic independence across models.

Contribution

It demonstrates that correlation functions in these systems satisfy PDEs related to random walk generators, revealing a shared asymptotic independence property.

Findings

Correlation functions follow PDEs derived from random walk generators

Asymptotic independence is established for many models

The approach links microscopic dynamics to macroscopic PDE behavior

Abstract

We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be written in terms of the generator of a two-dimensional random walk, whose jump rates are model dependent. From this, we deduce an asymptotic independence which is shared by many models.