Generalized law of iterated logarithm for the Lorentz gas with infinite horizon

Abstract

We obtain a generalized law of the iterated logarithm for a class of dependent processes with superdiffusive behaviour. Our results apply in particular to the Lorentz gas with infinite horizon.

Restructured, exposition is now more focused on results for the Lorentz gas. Proof of Lemma 5.4 (Lemma 4.4 in the previous version) corrected