## Bernoulli

• Bernoulli
• Volume 21, Number 3 (2015), 1824-1843.

### Extinction time for a random walk in a random environment

#### 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.

#### Article information

Source
Bernoulli, Volume 21, Number 3 (2015), 1824-1843.

Dates
Revised: December 2013
First available in Project Euclid: 27 May 2015

https://projecteuclid.org/euclid.bj/1432732038

Digital Object Identifier
doi:10.3150/14-BEJ627

Mathematical Reviews number (MathSciNet)
MR3352062

Zentralblatt MATH identifier
1332.60137

#### Citation

De Masi, Anna; Presutti, Errico; Tsagkarogiannis, Dimitrios; Vares, Maria Eulalia. Extinction time for a random walk in a random environment. Bernoulli 21 (2015), no. 3, 1824--1843. doi:10.3150/14-BEJ627. https://projecteuclid.org/euclid.bj/1432732038

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