The Annals of Probability

Brownian Survival Among Gibbsian Traps

Alain-Sol Sznitman

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Abstract

We consider Brownian motion evolving among killing traps. We develop a technique of "enlargement of obstacles." This technique allows us to replace given trap configurations by configurations of enlarged traps, when deriving upper estimates on the probability that Brownian motion survives. Applied in a context of random obstacles, this reduces the complexity of the description for the environment seen by Brownian motion. We apply the method to the case where traps are distributed according to a fairly general Gibbs measure and obtain a result in the spirit of Donsker-Varadhan's theorem on Wiener sausage asymptotics.

Article information

Source
Ann. Probab., Volume 21, Number 1 (1993), 490-508.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989413

Digital Object Identifier
doi:10.1214/aop/1176989413

Mathematical Reviews number (MathSciNet)
MR1207235

Zentralblatt MATH identifier
0769.60104

JSTOR
links.jstor.org

Subjects
Primary: 60K40: Other physical applications of random processes
Secondary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Keywords
Brownian motion killing traps principal eigenvalues Gibbs measures

Citation

Sznitman, Alain-Sol. Brownian Survival Among Gibbsian Traps. Ann. Probab. 21 (1993), no. 1, 490--508. doi:10.1214/aop/1176989413. https://projecteuclid.org/euclid.aop/1176989413


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