Abstract As Bleher (J. Stat. Phys. 66 (1): 315–373, 1992) observed the free flight vector of the
planar, infinite horizon, periodic Lorentz process S n∣ n= 0, 1, 2,… belongs to the non …

We show that if an infinite measure preserving system is well approximated on most of the
phase space by a system satisfying the local limit theorem, then the original system enjoys …

We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random
sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an …

In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the
idea of mixing for observables possessing an infinite-volume average. The idea is borrowed …

We perform numerical measurements of the moments of the position of a tracer particle in a
two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is …

Understanding the statistical properties of the aperiodic planar Lorentz gas stands as a
grand challenge in the theory of dynamical systems. Here we study a greatly simplified but …

It is a safe conjecture that most (not necessarily periodic) two-dimensional Lorentz gases
with finite horizon are recurrent. Here we formalize this conjecture by means of a stochastic …

We give a fairly complete characterization of the exact components of a large class of
uniformly expanding Markov maps of $\mathbb {R} $. Using this result, for a class of …

Mathematical theory of billiards is a fascinating subject providing a fertile source of new
problems as well as conjecture testing in dynamics, geometry, mathematical physics and …

Random walks and Lorentz processes serve as fundamental models for Brownian motion.
The study of random walks is a favorite object of probability theory, whereas that of Lorentz …