The Annals of Probability

Enlargement of Obstacles for the Simple Random Walk

Peter Antal

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Abstract

We consider a continuous time simple random walk moving among obstacles, which are sites (resp., bonds) of the lattice $Z^d$. We derive in this context a version of the technique of enlargement of obstacles developed by Sznitman in the Brownian case. This method gives controls on exponential moments of certain death times as well as good lower bounds for certain principal eigenvalues. We give an application to recover an asymptotic result of Donsker and Varadhan on the number of sites visited by the random walk and another application to the number of bonds visited by the random walk.

Article information

Source
Ann. Probab., Volume 23, Number 3 (1995), 1061-1101.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988174

Digital Object Identifier
doi:10.1214/aop/1176988174

Mathematical Reviews number (MathSciNet)
MR1349162

Zentralblatt MATH identifier
0839.60064

JSTOR
links.jstor.org

Subjects
Primary: 60J15
Secondary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Keywords
Random walk killing traps principal eigenvalues

Citation

Antal, Peter. Enlargement of Obstacles for the Simple Random Walk. Ann. Probab. 23 (1995), no. 3, 1061--1101. doi:10.1214/aop/1176988174. https://projecteuclid.org/euclid.aop/1176988174


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