Occupation time large deviations of two-dimensional symmetric simple exclusion process.
type: Item
instance of: scholarly article
title: Occupation time large deviations of two-dimensional symmetric simple exclusion process.
zbMATH Open document ID: 1061.60103
author: Chih-Chung Chang
author: C. Landim
author: Tzong-Yow Lee
published in: The Annals of Probability
publication date: 2004-09-15T00:00:00Z
review text: The article considers the nearest-neighbour symmetric simple exclusion process on the square lattice \( \mathbb{Z}^2 \). This process can be seen as follows. Distribute particle on \( \mathbb{Z}^2 \), such that each site is occupied by at most one particle. Each particle, independently from the others, waits a mean-\(1\) exponential time before it chooses one of its neighbour sites with uniform probability. If the site is unoccupied, the particle jumps to this site, otherwise, it stays where it is. Thus each lattice point is occupied by at most one particle. For this stochastic dynamics one has a one-parameter family of invariant states, the Bernoulli product measures with given probability density \( \alpha\in[0,1] \). This measure is obtained if one places at each site particle with probability \( \alpha \) independently from the others. A Bernoulli product measure is an ergodic, invariant, reversible state for the exclusion process. The occupation time at the origin is defined as the random proportion of time that the origin is occupied in a given time interval. This random variable converges almost surely for diverging time with respect to a Bernoulli product measure to the parameter \( \alpha \) of that measure. The authors prove a large deviations result for this occupation time at the origin for diverging time, where the decay rate is \( t/\log t \) in the time variable. This is the first example of an interacting particle system where the large deviations rate function associated to the occupation time can be explicitly computed. Second, the method of the proof is remarkable. The authors show that the large deviations in dimension two are related to the large deviations for the polar empirical measure (recall that in dimension one the large deviations of the occupation measure are related to the large deviations for the empirical measure in the hydrodynamical limit). The polar empirical measure is a random measure on \( \mathbb{R}_+ \), and for this article …
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 82C22
zbMATH DE Number: 2100730
zbMATH Keywords: exclusion process
zbMATH Keywords: large deviations
zbMATH Keywords: occupation time
zbMATH Keywords: polar empirical measure
zbMATH Keywords: hydrodynamic limit
reviewed by: Stefan Adams
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1079021460
OpenAlex ID: W2061670485
cites work: Symmetric exclusion processes: A comparison inequality and a large deviation result
cites work: Large deviations for the occupation times of independent particle systems
cites work: Large deviations from the hydrodynamical limit of mean zero asymmetric zero range processes
cites work: Q3757123
cites work: Large deviations for independent random walks
cites work: Large deviations for Poisson systems of independent random walks
cites work: Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes
cites work: Fluctuations des temps d'occupation d'un site dans l'exclusion simple symétrique. (Fluctuations in the occupation time of a site in simple symmetric exclusion)
cites work: Q4223675
cites work: Hydrodynamics and large deviation for simple exclusion processes
cites work: Occupation time large deviations for the symmetric simple exclusion process
cites work: Asymptotic results for super-Brownian motions and semilinear differential equations
DOI: 10.1214/AOP/1079021460
description: scientific article; zbMATH DE number 2100730