[Author]
Vysotsky V. V.
[Title]
A limit theorem for the position of a particle in Lorentz model
[AMS Subj-class]
60K37 Processes in random environments
[Abstract]
Consider a particle moving through a random medium. The medium
consists of immobile spherical obstacles of equal radii, randomly
distributed in $\R^3$. The particle is accelerated by a constant
external field; when colliding with an obstacle, the particle
inelastically reflects. We study the 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 $X(t)$. Its proof is based on the
functional CLT for Markov chains.
[Keywords]
Lorentz model, random medium, position of particle, FCLT for Markov chains,
limit theorems
[Comments]
LaTeX, Russian, 20 pp.
To be published in "Zapiski nauchnih seminarov POMI"
[Contact e-mail]
vysotsky@vv9034.spb.edu