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

PDF - Published Version Restricted to Registered users only Download (310kB)

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

Available Versions of this Item

• Extinction time for a random walk in a random environment. (deposited 24 Jun 2014 06:40)
  • Extinction time for a random walk in a random environment. (deposited 23 Jul 2015 11:45) [Currently Displayed]

View download statistics for this item

📧 Request an update