Scaling Limits of Additive Functionals of Interacting Particle Systems

Using the renormalization method introduced by the authors, we prove what we call the 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. © 2013 Wiley Periodicals, Inc.