Scaling limits of additive functionals of interacting particle systems

TL;DR

This paper establishes a local Boltzmann-Gibbs principle for one-dimensional conservative interacting particle systems using renormalization, leading to new scaling limits and a novel process related to the stochastic Burgers equation.

Contribution

It introduces a local Boltzmann-Gibbs principle for 1D systems and derives new scaling limits and a related process for the stochastic Burgers equation.

Findings

Derived scaling limits for additive functionals

Constructed a new process linked to the stochastic Burgers equation

Applied renormalization method to particle systems

Abstract

Using the renormalization method introduced in \cite{GJ}, we prove what we call the {\em local} Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension $d=1$. As applications of this result, we obtain various scaling limits of additive functionals of particle systems, like the occupation time of a given site or extensive additive fields of the dynamics. As a by-product of these results, we also construct a novel process, related to the stationary solution of the stochastic Burgers equation.