On the Boltzmann equation for the Lorentz gas

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

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99 Scopus citations


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
Issue number3
StatePublished - Sep 1 1983
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Boltzmann equation
  • Boltzmann-Grad limit
  • Lorentzmodel


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