On Some Random Billiards in a Tube with Superdiffusion

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 displacement of a particle, which marginally fails to have a second moment w.r.t. the invariant measure of the random billiard.