Journal of Mathematical Sciences

, Volume 139, Issue 3, pp 6520–6534 | Cite as

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

  • V. V. Vysotsky


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.


Markov Chain Invariant Measure Poisson Point Process Initial Speed Exponential Random Variable 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. V. Vysotsky
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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