Central Limit Theorem for a Class of Linear Systems

TL;DR

This paper proves a central limit theorem for the particle density in certain interacting particle systems in high dimensions, providing bounds on site density and overlap.

Contribution

It introduces a CLT for particle density in a class of systems, including the binary contact process, under specific integrability conditions.

Findings

Central limit theorem established for particle density in high dimensions

Upper bounds derived for site density and replica overlap

Applicable to systems like the binary contact process

Abstract

We consider a class of interacting particle systems with values in $[0,\8)^{\zd}$, of which the binary contact path process is an example. For $d \ge 3$ and under a certain square integrability condition on the total number of the particles, we prove a central limit theorem for the density of the particles, together with upper bounds for the density of the most populated site and the replica overlap.