Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap
dc.contributor.author | Majumdar, Satya N. | en_US |
dc.contributor.author | Comtet, Alain | en_US |
dc.contributor.author | Ziff, Robert M. | en_US |
dc.date.accessioned | 2006-09-11T15:42:48Z | |
dc.date.available | 2006-09-11T15:42:48Z | |
dc.date.issued | 2006-03 | en_US |
dc.identifier.citation | Majumdar, Satya N.; Comtet, Alain; Ziff, Robert M.; (2006). "Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap." Journal of Statistical Physics 122(5): 833-856. <http://hdl.handle.net/2027.42/45136> | en_US |
dc.identifier.issn | 1572-9613 | en_US |
dc.identifier.issn | 0022-4715 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/45136 | |
dc.description.abstract | 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 analytically. 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. | en_US |
dc.format.extent | 186430 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers-Plenum Publishers; Springer Science+Business Media, Inc. | en_US |
dc.subject.other | Adsorption to a Trap | en_US |
dc.subject.other | Diffusion | en_US |
dc.subject.other | Random Walk | en_US |
dc.subject.other | Wiener-Hopf | en_US |
dc.subject.other | Sparre Anderson Theorem | en_US |
dc.title | Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Michigan Center for Theoretical Physics and Department of Chemical Engineering, University of Michigan, Ann Arbor, MI, 48109-2136, USA | en_US |
dc.contributor.affiliationother | Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud. Bât, Orsay Cedex, 100. 91405, France | en_US |
dc.contributor.affiliationother | Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud. Bât, Orsay Cedex, 100. 91405, France; Institut Henri Poincaré, 11 rue Pierre et Marie Curie, Paris, 75005, France | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/45136/1/10955_2005_Article_9002.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s10955-005-9002-x | en_US |
dc.identifier.source | Journal of Statistical Physics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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