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 $c\exp \{-b{N}^{-2}t\}$, with $c$ and $b$ positive constants.

Published at http://dx.doi.org/10.3150/14-BEJ627 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Current reservoirs in the simple exclusion process
• Non equilibrium stationary state for the SEP with births and deaths
• Exponential rate of convergence in current reservoirs

Cited by in corpus (2)

• Fick law and sticky Brownian motions
• Exponential rate of convergence in current reservoirs