Scaling Limits of Additive Functionals of Interacting Particle Systems
Article first published online: 5 FEB 2013
Copyright © 2013 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 66, Issue 5, pages 649–677, May 2013
How to Cite
Gonçalves, P. and Jara, M. (2013), Scaling Limits of Additive Functionals of Interacting Particle Systems. Comm. Pure Appl. Math., 66: 649–677. doi: 10.1002/cpa.21441
- Issue published online: 25 FEB 2013
- Article first published online: 5 FEB 2013
- Manuscript Received: MAY 2011
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.