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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards

Texto completo
Autor(es):
Comets, Francis [1] ; Popov, Serguei [2]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] Univ Paris 07, UFR Math, F-75205 Paris 13 - France
[2] Univ Campinas UNICAMP, Inst Math Stat & Sci Computat, Dept Stat, BR-13083859 Campinas, SP - Brazil
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES; v. 48, n. 3, p. 721-744, AUG 2012.
Citações Web of Science: 6
Resumo

We consider a random walk in a stationary ergodic environment in Z, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right which implies that there are no ``traps.{''} We prove the law of large numbers with positive speed, as well as the ergodicity of the environment seen from the particle. Then, we consider Knudsen stochastic billiard with a drift in a random tube in R-d, d >= 3, which serves as environment. The tube is infinite in the first direction, and is a stationary and ergodic process indexed by the first coordinate. A particle is moving in-straight line inside the tube, and has random bounces upon hitting the boundary, according to the following modification of the cosine reflection law: the jumps in the positive direction are always accepted while the jumps in the negative direction may be rejected. Using the results for the random walk in random environment together with an appropriate coupling, we deduce the law of large numbers for the stochastic billiard with a drift. (AU)

Processo FAPESP: 09/08665-6 - Passeios aleatórios nas árvores e passeios aleatórios com ramificação
Beneficiário:Serguei Popov
Linha de fomento: Auxílio à Pesquisa - Regular