Open Access
2009 Survival time of random walk in random environment among soft obstacles
Nina Gantert, Serguei Popov, Marina Vachkovskaia
Author Affiliations +
Electron. J. Probab. 14: 569-593 (2009). DOI: 10.1214/EJP.v14-631


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 <i>d</i>-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).


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Nina Gantert. Serguei Popov. Marina Vachkovskaia. "Survival time of random walk in random environment among soft obstacles." Electron. J. Probab. 14 569 - 593, 2009.


Accepted: 20 January 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1192.60112
MathSciNet: MR2480554
Digital Object Identifier: 10.1214/EJP.v14-631

Primary: 60K37

Keywords: branching random walks in random environment , confinement of RWRE , nestling RWRE , quenched and annealed tails , survival time

Vol.14 • 2009
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