On the Boltzmann equation for the Lorentz gas

C. Boldrighini, L. A. Bunimovich, Ya G. Sinai

Research output: Contribution to journalArticle

79 Scopus citations

Abstract

We consider the Boltzmann-Grad limit for the Lorentz, or wind-tree, model. We prove that if ω is a fixed configuration of scatterer centers belonging to a set of full measure with respect to the Poisson distribution with parameter λ>0, then the evolution of an initial a.c. particle density tends in the Boltzmann-Grad limit to the solution of the Boltzmann equation for the model. As an intermediate step we prove that the process of the free path lengths and impact parameters induced by the Lebesgue measure on a small region tends to a limiting independent process.

Original languageEnglish (US)
Pages (from-to)477-501
Number of pages25
JournalJournal of Statistical Physics
Volume32
Issue number3
DOIs
StatePublished - Sep 1 1983
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Boltzmann equation
  • Boltzmann-Grad limit
  • Lorentzmodel

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