Journal of Mathematical Sciences

, Volume 139, Issue 3, pp 6520–6534

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

• V. V. Vysotsky
Article

## Abstract

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.

## Keywords

Markov Chain Invariant Measure Poisson Point Process Initial Speed Exponential Random Variable
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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