A functional limit theorem for the position of a particle in the Lorentz model

V. V. Vysotsky

Research output: Contribution to journalArticle


We consider a particle moving through a medium under a constant external field. The medium consists of immobile spherical obstacles of equal radii randomly distributed in ℝ3. When the particle collides with an obstacle, it reflects inelastically, with restitution coefficient α , (0, 1). We study the asymptotics of X(t), the position of the particle at time t, as t → ∞. The main result is a functional limit theorem for X(t). Its proof is based on the functional CLT for Markov chains. Bibliography: 10 titles.

Original languageEnglish (US)
Pages (from-to)6520-6534
Number of pages15
JournalJournal of Mathematical Sciences
Issue number3
StatePublished - Dec 1 2006


ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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