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

dc.creatorComets, F
dc.creatorPopov, S
dc.date2012
dc.dateAUG
dc.date2014-07-30T13:51:38Z
dc.date2015-11-26T16:40:56Z
dc.date2014-07-30T13:51:38Z
dc.date2015-11-26T16:40:56Z
dc.date.accessioned2018-03-28T23:25:01Z
dc.date.available2018-03-28T23:25:01Z
dc.identifierAnnales De L Institut Henri Poincare-probabilites Et Statistiques. Inst Mathematical Statistics, v. 48, n. 3, n. 721, n. 744, 2012.
dc.identifier0246-0203
dc.identifierWOS:000306680800006
dc.identifier10.1214/11-AIHP439
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/55296
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/55296
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1272765
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionWe 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.
dc.description48
dc.description3
dc.description721
dc.description744
dc.descriptionCNRS [UMR 7599]
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionPRONEX "Probabilidade e Modelagem Estocastica"
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionCNRS [UMR 7599]
dc.descriptionFAPESP [2009/52379-8, 2009/08665-6]
dc.descriptionCNPq [300886/2008-0, 472431/2009-9]
dc.languageen
dc.publisherInst Mathematical Statistics
dc.publisherCleveland
dc.publisherEUA
dc.relationAnnales De L Institut Henri Poincare-probabilites Et Statistiques
dc.relationAnn. Inst. Henri Poincare-Probab. Stat.
dc.rightsaberto
dc.sourceWeb of Science
dc.subjectCosine law
dc.subjectStochastic billiard
dc.subjectKnudsen random walk
dc.subjectRandom medium
dc.subjectRandom walk in random environment
dc.subjectUnbounded jumps
dc.subjectStationary ergodic environment
dc.subjectRegenerative structure
dc.subjectPoint of view of the particle
dc.subjectAsymptotic-behavior
dc.subjectStrip
dc.titleBallistic regime for random walks in random environment with unbounded jumps and Knudsen billiards
dc.typeArtículos de revistas


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