Density fluctuations for a zero-range process on the percolation cluster

TL;DR

This paper proves that the density fluctuations of a zero-range process on a supercritical percolation cluster follow a generalized Ornstein-Uhlenbeck process, advancing understanding of stochastic processes on complex random structures.

Contribution

It establishes the limiting behavior of density fluctuations for zero-range processes on percolation clusters, a novel result in stochastic process theory on random media.

Findings

Density fluctuations converge to a generalized Ornstein-Uhlenbeck process

Results apply to supercritical percolation clusters in $b R^d$

Advances understanding of stochastic dynamics on random structures

Abstract

We prove that the density fluctuations for a zero-range process evolving on the supercritical percolation cluster are given by a generalized Ornstein-Uhlenbeck process in the space of distributions $\mc S'(\bb R^d)$.