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

#### 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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