ABSTRACT:

It is a safe---albeit imprecise---conjecture that most Lorentz gases in 2D are recurrent. We formalize this conjecture by means of a stochastic ensemble of Lorentz gases, in which i.i.d. random scatterers are placed in each cell of a co-compact lattice in the plane. We give results towards showing that recurrence is an almost sure property (topological typicality and a 0-1 law that holds in every dimension). The mathematical machinery, including an application of a beautiful theorem by Schmidt and Conze, can be pushed further in the case of simpler systems having the same structure. These include the so-called persistent random walks in random environment. For a large class of them we prove almost sure recurrence.