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July, 1995 Enlargement of Obstacles for the Simple Random Walk
Peter Antal
Ann. Probab. 23(3): 1061-1101 (July, 1995). DOI: 10.1214/aop/1176988174


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.


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Peter Antal. "Enlargement of Obstacles for the Simple Random Walk." Ann. Probab. 23 (3) 1061 - 1101, July, 1995.


Published: July, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0839.60064
MathSciNet: MR1349162
Digital Object Identifier: 10.1214/aop/1176988174

Primary: 60J15
Secondary: 82D30

Keywords: killing traps , principal eigenvalues , Random walk

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • July, 1995
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