Recurrence for quenched random Lorentz tubes

Abstract

We consider the billiard dynamics in a strip-like set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called `quenched random Lorentz tube'. We prove that, under general conditions, almost every system in the ensemble is recurrent.

23 pages, 8 figures. Version published on Chaos, vol. 20 (2010) + correction of small erratum in condition (A3)

References in corpus (7)

• Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels
• Increasing thermoelectric efficiency towards the Carnot limit
• Quenched CLT for random toral automorphism
• Typicality of recurrence for Lorentz gases
• Aperiodic Lorentz gas: recurrence and ergodicity
• Recurrence for persistent random walks in two dimensions
• Central Limit Theorem and recurrence for random walks in bistochastic random environments

Cited by in corpus (8)

• Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
• Random walks in a one-dimensional Lévy random environment
• Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties
• A local limit theorem for a transient chaotic walk in a frozen environment
• Recurrence in generic staircases
• Classical Motion in Random Potentials
• Statistical properties of Lorentz gases on aperiodic tilings, Part 1
• Dynamical random walk on the integers with a drift