Electronic Journal of Probability
- Electron. J. Probab.
- Volume 6 (2001), paper no. 1, 10 pp.
A Note on Limiting Behaviour of Disastrous Environment Exponents
Abstract
We consider a random walk on the $d$-dimensional lattice and investigate the asymptotic probability of the walk avoiding a "disaster" (points put down according to a regular Poisson process on space-time). We show that, given the Poisson process points, almost surely, the chance of surviving to time $t$ is like $e^{-\alpha \log (\frac1k) t } $, as $t$ tends to infinity if $k$, the jump rate of the random walk, is small.
Article information
Source
Electron. J. Probab., Volume 6 (2001), paper no. 1, 10 pp.
Dates
Accepted: 5 January 2001
First available in Project Euclid: 19 April 2016
Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461097631
Digital Object Identifier
doi:10.1214/EJP.v6-74
Mathematical Reviews number (MathSciNet)
MR1814217
Zentralblatt MATH identifier
0976.60093
Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Keywords
Random walk disaster point Poisson process
Rights
This work is licensed under aCreative Commons Attribution 3.0 License.
Citation
Mountford, Thomas. A Note on Limiting Behaviour of Disastrous Environment Exponents. Electron. J. Probab. 6 (2001), paper no. 1, 10 pp. doi:10.1214/EJP.v6-74. https://projecteuclid.org/euclid.ejp/1461097631
