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Extinction time for a random walk in a random environment

journal contribution
posted on 2023-06-08, 21:46 authored by Anna De Masi, Errico Presutti, Dimitrios Tsagkarogiannis, Maria Eulalia Vares
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 ?ux from N to -N. Its evolution is in?uenced by the presence of the random walk and in turns it a?ects 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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Bernoulli

ISSN

1350-7265

Publisher

Bernoulli Society for Mathematical Statistics and Probability

Issue

3

Volume

21

Page range

1824-1843

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2015-07-23

First Compliant Deposit (FCD) Date

2015-07-23

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