Survival time of random walk in random environment among soft obstacles

Author(s)

Gantert, Nina ^{[1, 2]} ; Popov, Serguei ^[3] ; Vachkovskaia, Marina ^[4]

Affiliation

^[1] CeNos Ctr Nonlinear Sci, D-48149 Munster - Germany

^[2] Fachbereich Math & Informat, Inst Stat Math, D-48149 Munster - Germany

^[3] Univ Sao Paulo, Inst Matemat & Estat, BR-05508900 Sao Paulo - Brazil

^[4] Univ Estadual Campinas, Dept Estat, Inst Matemat Estat & Comp Cient, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: ELECTRONIC JOURNAL OF PROBABILITY; v. 14, p. 569-593, FEB 24 2009.
• Web of Science Citations: 2

Abstract

We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d. random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched and annealed bounds on the tails of the survival time in the general d-dimensional case. We then consider a simplified one-dimensional model (where transition probabilities and obstacles are independent and the RWRE only moves to neighbour sites), and obtain finer results for the tail of the survival time. In addition, we study also the ``mixed{''} probability measures (quenched with respect to the obstacles and annealed with respect to the transition probabilities and vice-versa) and give results for tails of the survival time with respect to these probability measures. Further, we apply the same methods to obtain bounds for the tails of hitting times of Branching Random Walks in Random Environment (BRWRE). (AU)

• FAPESP's process: 04/07276-2 - Stochastic Modelling of Interacting Systems
• Grantee: Luiz Renato Gonçalves Fontes
• Support Opportunities: Research Projects - Thematic Grants