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 survival probability up to time $t$ which goes as $c\exp\{-b N^{-2} t\}$, with $c$ and $b$ positive constants.

Extinction time for a random walk in a random environment

DE MASI, Anna;E. Presutti;
2015-01-01

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 survival probability up to time $t$ which goes as $c\exp\{-b N^{-2} t\}$, with $c$ and $b$ positive constants.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/16447
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