Electronic Journal of Probability

A Note on Limiting Behaviour of Disastrous Environment Exponents

Thomas Mountford

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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


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References

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