Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/58758
Type: Artigo de periódico
Title: QUENCHED INVARIANCE PRINCIPLE FOR THE KNUDSEN STOCHASTIC BILLIARD IN A RANDOM TUBE
Author: Comets, F
Popov, S
Schutz, GM
Vachkovskaia, M
Abstract: We consider a stochastic billiard in a random tube which stretches to infinity in the direction of the first coordinate. This random tube is stationary and ergodic, and also it is supposed to be in some sense well behaved. The stochastic billiard can be described as follows: when strictly inside the tube, the particle moves straight with constant speed. Upon hitting the boundary, it is reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. We also consider the discrete-time random walk formed by the particle's positions at the moments of hitting the boundary. Under the condition of existence of the second moment of the projected jump length with respect to the stationary measure for the environment seen from the particle, we prove the quenched invariance principles for the projected trajectories of the random walk and the stochastic billiard.
Subject: Cosine law
Knudsen random walk
stochastic homogenization
invariance principle
random medium
random conductances
random walks in random environment
Country: EUA
Editor: Inst Mathematical Statistics
Rights: aberto
Identifier DOI: 10.1214/09-AOP504
Date Issue: 2010
Appears in Collections:Unicamp - Artigos e Outros Documentos

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