QUENCHED INVARIANCE PRINCIPLE FOR THE KNUDSEN STOCHASTIC BILLIARD IN A RANDOM TUBE

Autor(es)

Comets, Francis ^[1] ; Popov, Serguei ^[2] ; Schuetz, Gunter M. ^[3] ; Vachkovskaia, Marina ^[2]

Afiliação do(s) autor(es)

^[1] Univ Paris Diderot Paris 7, UFR Math, F-75205 Paris 13 - France

^[2] Univ Estadual Campinas, UNICAMP, Campinas, SP - Brazil

^[3] Forschungszentrum Julich, Inst Festkorperforsch, D-52425 Julich - Germany

• Tipo de documento: Artigo Científico
• Fonte: ANNALS OF PROBABILITY; v. 38, n. 3, p. 1019-1061, MAY 2010.
• Citações Web of Science: 9

Resumo

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. (AU)

• Processo FAPESP: 04/07276-2 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Luiz Renato Gonçalves Fontes
• Modalidade de apoio: Auxílio à Pesquisa - Temático