Densities of short random uniform walks

Title: Densities of short random uniform walks
Creator: Borwein, Jonathan M.; Straub, Armin; Wan, James; Zudilin, W.
Relation: Canadian Journal of Mathematics Vol. 64, Issue 5, p. 961-990
Publisher Link: http://dx.doi.org/10.4153/CJM-2011-079-2
Publisher: University of Toronto Press
Resource Type: journal article
Date: 2012
Description: We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and, less completely, those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.
Subject: random walks; hypergeometric functions; Mahler measure; random steps
Identifier: http://hdl.handle.net/1959.13/934776
Identifier: uon:11904
Identifier: ISSN:0008-414X
Language: eng
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