Geodesic
A limit theorem for the position of a~particle in the Lorentz model
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 42-68

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Consider a particle moving through a random medium. The medium consists of spherical obstacles of equal radii, randomly distributed in $\mathbb R^3$. The particle is accelerated by a constant external field. When colliding with an obstacle, the particle inelastically reflects. We study asymptotics of $X(t)$, which denotes the position of the particle at time $t$, as $t\to\infty$. The result is a limit theorem for $X(t)$. Our proof is based on functional CLT for Markov chains. 
@article{ZNSL_2005_328_a3,
     author = {V. V. Vysotsky},
     title = {A limit theorem for the position of a~particle in the {Lorentz} model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {42--68},
     publisher = {mathdoc},
     volume = {328},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a3/}
}
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V. V. Vysotsky. A limit theorem for the position of a~particle in the Lorentz model. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 42-68. http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a3/