Large deviations for noninteracting infinite particle systems
type: Item
instance of: scholarly article
title: Large deviations for noninteracting infinite particle systems
zbMATH Open document ID: 0661.60046
author: Tzong-Yow Lee
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: Let \(X=\{x_ i\}\) stand for a point configuration, \(w=\{w_ i(s)\}\) for the trajectory of a configuration, and \(P_{a,b}\) \((P_ X\), resp.) denote the probability distribution of the particle system with initial distribution \(\mu_{a,b}=\mu_{a+b \exp (x)}\quad (\delta_ X,\quad resp.).\) The author considers Brownian motion with constant drift and proves large deviation rates for the empirical density \[ D_{t,w}(K)=t^{-1}\int^{1}_{0}\sum_{i}I_ K(w_ i(s))ds\quad (K\subset R,\quad measurable) \] under \(P_{a,b}\) (Section 1) as well as under \(P_ X\) (Section 2). Initially a lower bound is found for the rate function, then a cumulant generating function estimation yields an upper bound, and finally the equivalence of upper and lower bounds is shown. At the end of the paper the author contrasts his model to that in the paper of \textit{M. D. Donsker} and \textit{S. R. S. Varadhan}, J. Stat. Phys. 46, 1195-1232 (1987), bearing the same title.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 4080520
zbMATH Keywords: Brownian motion
zbMATH Keywords: large deviation rates
zbMATH Keywords: empirical density
zbMATH Keywords: rate function
zbMATH Keywords: equivalence of upper and lower bounds
reviewed by: Elisaveta Pancheva
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991582
OpenAlex ID: W2079041245
DOI: 10.1214/AOP/1176991582
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description: scientific article; zbMATH DE number 4080520