Scaling limits of additive functionals of interacting 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.

24 pages, no figures, accepted for publication in "Communications on Pure and Applied Mathematics"

References in corpus (3)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Non equilibrium current fluctuations in stochastic lattice gases
• Universality of KPZ equation