caa a22 4500 467892741 CHVBK 20180406152753.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10955-005-9002-x doi (NATIONALLICENCE)springer-10.1007/s10955-005-9002-x Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap [Elektronische Daten] [Satya Majumdar, Alain Comtet, Robert Ziff] 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. Springer Science + Business Media, Inc., 2006 Random walk nationallicence adsorption to a trap nationallicence Wiener-Hopf nationallicence diffusion nationallicence Sparre Anderson theorem nationallicence Majumdar Satya Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud. Bât, 100. 91405, Orsay Cedex, France aut Comtet Alain Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud. Bât, 100. 91405, Orsay Cedex, France aut Ziff Robert Michigan Center for Theoretical Physics and Department of Chemical Engineering, University of Michigan, 48109-2136, Ann Arbor, MI, USA aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/5(2006-03-01), 833-856 0022-4715 122:5<833 2006 122 10955 https://doi.org/10.1007/s10955-005-9002-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-9002-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Majumdar Satya Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud. Bât, 100. 91405, Orsay Cedex, France aut NATIONALLICENCE 700 1- Comtet Alain Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud. Bât, 100. 91405, Orsay Cedex, France aut NATIONALLICENCE 700 1- Ziff Robert Michigan Center for Theoretical Physics and Department of Chemical Engineering, University of Michigan, 48109-2136, Ann Arbor, MI, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/5(2006-03-01), 833-856 0022-4715 122:5<833 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer