First occurrence time of a large density fluctuation for a system of independent random walks
type: Item
instance of: scholarly article
title: First occurrence time of a large density fluctuation for a system of independent random walks
zbMATH Open document ID: 0982.60036
DOI: 10.1016/S0246-0203(00)00129-1
author: Amine Asselah
author: Paolo Dai Pra
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2002-03-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77663
review text: A Poisson distributed number of particles is assigned to each site of the \(d\)-dimensional integer lattice. The mean number of particles is the same at all sites. The assignments are done independently. Then each particle starts a continuous time symmetric nearest neighbors random walk. The initial distribution is stationary for the motion. The authors study the first time \(T_n\) that a hypercube of volume \(n^d\) is occupied by more than \(\rho'n^d\) particles, where \(\rho'>\rho\) (a large deviation of the density of particles in the hypercube). They prove that as \(n\) goes to infinity, the time conveniently normalized converges to an exponentially distributed random variable.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1501490
zbMATH Keywords: independent random walks
zbMATH Keywords: exponential approximation
zbMATH Keywords: tail estimates
reviewed by: Pablo A. Ferrari
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1501490