## Electronic Journal of Probability

### Survival time of random walk in random environment among soft obstacles

#### 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 <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).

#### Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 22, 569-593.

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

https://projecteuclid.org/euclid.ejp/1464819483

Digital Object Identifier
doi:10.1214/EJP.v14-631

Mathematical Reviews number (MathSciNet)
MR2480554

Zentralblatt MATH identifier
1192.60112

Subjects
Primary: 60K37: Processes in random environments

Rights

#### Citation

Gantert, Nina; Popov, Serguei; Vachkovskaia, Marina. Survival time of random walk in random environment among soft obstacles. Electron. J. Probab. 14 (2009), paper no. 22, 569--593. doi:10.1214/EJP.v14-631. https://projecteuclid.org/euclid.ejp/1464819483

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