Life and Death in a Cage and at the Edge of a Cliff
arXiv:cond-mat/9502041 · doi:10.1119/1.18152
Abstract
The survival probabilities of a ``prisoner'' diffusing in an expanding cage and a ``daredevil'' diffusing at the edge of a receding cliff are investigated. When the diffuser reaches the boundary, he dies. For ``marginal'' boundary motion, i.e., the cage length grows as or the cliff location recedes as and the daredevil diffuses within the domain , the survival probability of the diffuser exhibits non-universal power-law behavior, $S(t)\sim t^{-\b}$, which depends on the relative rates of boundary and diffuser motion. Heuristic approaches are applied for the cases of ``slow'' and ``fast'' boundary motion which yield approximate expressions for $\b$. An asymptotically exact analysis of these two problems is also performed and the approximate expressions for $\b$ coincide with the exact results for nearly entire range of possible boundary motions.
arXiv comment11 pages, plain TeX, 1 figure (not included), submitted to J. Stat. Phys
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