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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## 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 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 |
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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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