Large deviations for systems of noninteracting recurrent particles
type: Item
instance of: scholarly article
title: Large deviations for systems of noninteracting recurrent particles
zbMATH Open document ID: 0664.60032
author: Tzong-Yow Lee
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: We consider noninteracting systems of infinite particles each of which follows an irreducible, null recurrent Markov process and prove a large deviation principle for the empirical density. The expected occupation time (up to time N) of this Markov process, named as h(N), plays an essential role in our result. We impose on h(N) a regularly varying property as \(N\to \infty\), which a large class of transition probabilities does satisfy. Some features of our result are: (a) The large deviation tails decay like \(\exp [-Nh^{-1}(N)I(\cdot)]\), more slowly than the known exp[-NI(\(\cdot)]\) type of decay in transient situations. (b) Our rate function I(\(\lambda\) (\(\cdot))\) equals infinity unless \(\lambda\) (\(\cdot)\) is an invariant distribution. (c) Our rate function is explicit and is rather insensitive to the underlying Markov process. For instance, if we randomized the time steps of a Markov chain by exponential waiting time of mean 1, the resultant system obeys exactly the same large deviation principle.
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 4086648
zbMATH Keywords: recurrence
zbMATH Keywords: systems of infinite particles
zbMATH Keywords: large deviation principle for the empirical density
zbMATH Keywords: occupation time
zbMATH Keywords: invariant distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991493
OpenAlex ID: W2041950785
DOI: 10.1214/AOP/1176991493
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description: scientific article; zbMATH DE number 4086648