Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap

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dc.creatorMajumdar, Satya N.
dc.creatorComtet, Alain
dc.creatorZiff, Robert M.
dc.date2005-09-23
dc.date2005-10-27
dc.date.accessioned2026-07-07T06:41:51Z
dc.date.available2026-07-07T06:41:51Z
dc.descriptionTwo random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived explicitly. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.
dc.descriptionTwo figs. Accepted for publication, Journal of Statistical Physics
dc.identifierhttps://arxiv.org/abs/cond-mat/0509613
dc.identifierhttp://arxiv.org/abs/cond-mat/0509613
dc.identifierJournal of Statistical Physics 122, 833-856 (2006)
dc.identifierdoi:10.1007/s10955-005-9002-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101822
dc.subjectStatistical Mechanics
dc.titleUnified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
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