2004/10/17 by Marco Lenci, MARCO LENCI · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Geometry and complex manifolds #Stochastic processes and statistical mechanics #math-ph #math.DS #math.MP #msc:37A40 #msc:37D50 #msc:60K37 #nlin.CD
paper · pdf · doi:10.1017/s0143385706000022
published as Ergodic Theory Dynam. Systems 26 (2006), no. 3, 799-820 · 22 pages, 5 figures
arxiv created 2004/10/17 · openalex publication_date 2006/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 ensemble of Lorentz gases, in which independent identically distributed random scatterers are placed in each cell of a co-compact lattice in the plane. We prove that the typical Lorentz gas, in the sense of Baire, is recurrent, and give results in the direction of showing that recurrence is an almost sure property (including a zero--one law that holds in every dimension). A few toy models illustrate the extent of these results.