Extinction time for a random walk in a random environment

De Masi, Anna, Presutti, Errico, Tsagkarogiannis, Dimitrios and Vares, Maria Eulalia (2015) Extinction time for a random walk in a random environment. Bernoulli, 21 (3). pp. 1824-1843. ISSN 1350-7265

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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{−bN−2 t}, with c and b positive constants.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Dimitrios Tsagkarogiannis
Date Deposited: 23 Jul 2015 11:45
Last Modified: 07 Mar 2017 08:07
URI: http://sro.sussex.ac.uk/id/eprint/55702

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