Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains

dc.creatorMenshikov, MV
dc.creatorVachkovskaia, M
dc.creatorWade, AR
dc.date2008
dc.dateSEP
dc.date2014-11-17T02:06:06Z
dc.date2015-11-26T16:35:16Z
dc.date2014-11-17T02:06:06Z
dc.date2015-11-26T16:35:16Z
dc.date.accessioned2018-03-28T23:17:41Z
dc.date.available2018-03-28T23:17:41Z
dc.identifierJournal Of Statistical Physics. Springer, v. 132, n. 6, n. 1097, n. 1133, 2008.
dc.identifier0022-4715
dc.identifierWOS:000258675200006
dc.identifier10.1007/s10955-008-9578-z
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/55115
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/55115
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/55115
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1271455
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionWe study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process originates with ideal gas models in the Knudsen regime, with particles reflecting off microscopically rough surfaces. We classify the process into recurrent and transient cases. We also give almost-sure results on the long-term behaviour of the location of the particle, including a super-diffusive rate of escape in the transient case. A key step in obtaining our results is to relate our process to an instance of a one-dimensional stochastic process with asymptotically zero drift, for which we prove some new almost-sure bounds of independent interest. We obtain some of these bounds via an application of general semimartingale criteria, also of some independent interest.
dc.description132
dc.description6
dc.description1097
dc.description1133
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionHeilbronn Institute for Mathematical Research
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFAPESP [07/50459-9, 04/07276-02]
dc.descriptionCNPq [304561/2006-1, 471925/2006-3]
dc.languageen
dc.publisherSpringer
dc.publisherNew York
dc.publisherEUA
dc.relationJournal Of Statistical Physics
dc.relationJ. Stat. Phys.
dc.rightsfechado
dc.rightshttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dc.sourceWeb of Science
dc.subjectstochastic billiards
dc.subjectrarefied gas dynamics
dc.subjectKnudsen random walk
dc.subjectrandom reflections
dc.subjectrecurrence/transience
dc.subjectLamperti problem
dc.subjectalmost-sure bounds
dc.subjectbirth-and-death chain
dc.subjectRandom-walks
dc.subjectInfinite Cusp
dc.titleAsymptotic behaviour of randomly reflecting billiards in unbounded tubular domains
dc.typeArtículos de revistas


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