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

V. V. Vysotsky

doi:10.1007/s10958-006-0369-2

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

V. V. Vysotsky

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › 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.

Original language	English (US)
Pages (from-to)	6520-6534
Number of pages	15
Journal	Journal of Mathematical Sciences
Volume	139
Issue number	3
DOIs	https://doi.org/10.1007/s10958-006-0369-2
State	Published - Dec 1 2006

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ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Applied Mathematics

Cite this

Vysotsky, V. V. (2006). A functional limit theorem for the position of a particle in the Lorentz model. Journal of Mathematical Sciences, 139(3), 6520-6534. https://doi.org/10.1007/s10958-006-0369-2

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10.1007/s10958-006-0369-2