A functional limit theorem for the position of a particle in the Lorentz model |
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Authors: | V V Vysotsky |
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Institution: | (1) St. Petersburg State University, St. Petersburg, Russia |
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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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 42–68.
An erratum to this article is available at . |
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Keywords: | |
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