Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap
| Autor: | Alain Comtet, Satya N. Majumdar, Robert M. Ziff |
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| Rok vydání: | 2006 |
| Předmět: |
Physics
Mathematical analysis Extrapolation Flux Boundary (topology) Statistical and Nonlinear Physics Context (language use) Random walk 01 natural sciences 010305 fluids & plasmas Dimension (vector space) Random walker algorithm 0103 physical sciences 010306 general physics Constant (mathematics) Mathematical Physics |
| Zdroj: | Journal of Statistical Physics. 122:833-856 |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-005-9002-x |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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