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August 2015 Extinction time for a random walk in a random environment
Anna De Masi, Errico Presutti, Dimitrios Tsagkarogiannis, Maria Eulalia Vares
Bernoulli 21(3): 1824-1843 (August 2015). DOI: 10.3150/14-BEJ627

Abstract

We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random walk and in turn it affects the jump rates of the random walk in a neighborhood of the endpoints, determining also the rate for the random walk to die. We prove an upper bound (uniform in $N$) for the survival probability up to time $t$ which goes as $c\exp\{-bN^{-2}t\}$, with $c$ and $b$ positive constants.

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Anna De Masi. Errico Presutti. Dimitrios Tsagkarogiannis. Maria Eulalia Vares. "Extinction time for a random walk in a random environment." Bernoulli 21 (3) 1824 - 1843, August 2015. https://doi.org/10.3150/14-BEJ627

Information

Received: 1 March 2013; Revised: 1 December 2013; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1332.60137
MathSciNet: MR3352062
Digital Object Identifier: 10.3150/14-BEJ627

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 3 • August 2015
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