On some random billiards in a tube with superdiffusion

arXiv (Cornell University)

Abstract

We consider a class of random billiards in a tube, where reflection angles at collisions with the boundary of the tube are random variables rather than deterministic (and elastic) quantities. We obtain a (non-standard) Central Limit Theorem for the horizontal displacement of a particle, which marginally fails to have a second moment w.r.t.\ the invariant measure of the random billiard.

Authors 3

1. Henk Bruin

   University of Vienna

   Affiliation as printed

   Faculty of Mathematics , University of Vienna , Oskar Morgensternplatz 1 , 1090 Vienna , Austria;

2. Niels Kolenbrander Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut , University of Leiden , Einsteinweg 55 , 2333 CC Leiden , The Netherlands ;

3. Dalia Terhesiu Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut , University of Leiden , Einsteinweg 55 , 2333 CC Leiden , The Netherlands ;