A Functional Limit Theorem for the Position of a Particle in a Lorentz Type Model

#### V. Vysotsky

2006, v.12, №4, 767-790

ABSTRACT

Consider a particle moving through a random medium, which consists of spherical obstacles, 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 functional limit theorem for $X(t)$.

Keywords: Lorentz model,motion in random medium,functional centrallimit theorem for Markov chains,limit theorems