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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

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Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1103.3722v4
Date
2013
Journal name
Communications on Pure and Applied Mathematics
Volume
66
Number
5
Publisher
Wiley
Pages
649-677
Publication identifier
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Author(s)
Gonçalves, Patricia
Jara, Milton
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 / Keywords
stochastic Burgers equation; Boltzmann-Gibbs principle