Scaling Limits of Additive Functionals of Interacting Particle Systems
Gonçalves, Patricia; Jara, Milton (2013), Scaling Limits of Additive Functionals of Interacting Particle Systems, Communications on Pure and Applied Mathematics, 66, 5, p. 649-677. http://dx.doi.org/10.1002/cpa.21441
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1103.3722v4
Journal nameCommunications on Pure and Applied Mathematics
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Abstract (EN)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.
Subjects / Keywordsstochastic Burgers equation; Boltzmann-Gibbs principle
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