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Scaling Limits of Additive Functionals of Interacting Particle Systems
Author(s) -
Gonçalves Patrícia,
Jara Milton
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21441
Subject(s) - mathematics , scaling , statistical physics , particle system , dimension (graph theory) , product (mathematics) , renormalization , particle (ecology) , mathematical physics , physics , pure mathematics , computer science , oceanography , geometry , geology , operating system
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.