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TitleOccupation times of exclusion processes
Author(s)Gonçalves, Patrícia
KeywordsAdditive functional
Exclusion processes
Issue date2014
JournalSpringer Proceedings in Mathematics and Statistics
Abstract(s)In this paper we consider exclusion processes $\{\eta_t: t\geq{0}\}$ evolving on the one-dimensional lattice $\mathbb{Z}$, under the diffusive time scale $tn^2$ and starting from the invariant state $\nu_\rho$ - the Bernoulli product measure of parameter $\rho\in{[0,1]}$. Our goal consists in establishing the scaling limits of the additive functional $\Gamma_t:=\int_{0}^{tn^2} \eta_s(0)\, ds$ - {\em{ the occupation time of the origin}}. We present a method, recently introduced in \cite{G.J.}, from which a {\em{local Boltzmann-Gibbs Principle}} can be derived for a general class of exclusion processes. In this case, this principle says that $\Gamma_t$ is very well approximated to the additive functional of the density of particles. As a consequence, the scaling limits of $\Gamma_t$ follow from the scaling limits of the density of particles. As examples we present the mean-zero exclusion, the symmetric simple exclusion and the weakly asymmetric simple exclusion. For the latter under a strong asymmetry regime, the limit of $\Gamma_t$ is given in terms of the solution of the KPZ equation.
TypeConference paper
AccessOpen access
Appears in Collections:CMAT - Artigos em atas de conferências e capítulos de livros com arbitragem / Papers in proceedings of conferences and book chapters with peer review

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