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A Note on Limiting Behaviour of Disastrous Environment Exponents
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Thomas S. Mountford, University of California, Los Angeles
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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.
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Full text: PDF
Pages: 1-10
Published on: January 5, 2001
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Electronic Journal of Probability. ISSN: 1083-6489 |
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