Extinction time for a random walk in a random environment

De Masi, Anna and Presutti, Errico and Tsagkarogiannis, Dimitrios and Vares, Maria Eulalia (2013) Extinction time for a random walk in a random environment. (Submitted)

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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 turns 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 probability of extinction by time $t$ which goes as $c\exp\{-b N^{-2} t\}$, $c$ and $b$ positive constants.

Item Type: Article
Depositing User: Dr. Dimitrios Tsagkarogiannis
Date Deposited: 01 Apr 2013 09:01
Last Modified: 13 Apr 2018 17:13
URI: http://preprints.acmac.uoc.gr/id/eprint/224

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