Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-09-23
Journal of Statistical Physics 122, 833-856 (2006)
Physics
Condensed Matter
Statistical Mechanics
Two figs. Accepted for publication, Journal of Statistical Physics
Scientific paper
10.1007/s10955-005-9002-x
Two 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.
Comtet Alain
Majumdar Satya N.
Ziff Robert M.
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