Vlad Vysotsky
University of Delaware
Title: A limit theorem for the trajectory of a particle moving in random medium.
Consider a particle moving through a random medium and driven by a constant external field. The medium consists of immobile spherical obstacles, randomly distributed in R^d. When colliding with obstacles, the particle inelastically reflects and continues its motion. This model is called the Lorentz model; we are interested in the asymptotics of X(t), which denotes the position of the particle at time t, as t tends to infinity. The Lorentz model, however, is extremely complicated to analyze, therefore we introduce its approximation, called the Markov approximation of the Lorentz model (MALM, in short), and study the relation between the models. For the MALM model, we study the asymptotical position of the particle. Our main result is a functional limit theorem for X(t).
©2008, Department of Mathematical Sciences
Last Modified: September 25, 2008