A Brief Introduction

Abstract

The main theme of this series of lectures are “Random motions in random media”. The subject gathers a variety of probabilistic models often originated from physical sciences such as solid state physics, physical chemistry, oceanography, biophysics—, in which typically some diffusion mechanism takes place in an Mhomogeneous medium. Randomness appears at two levels. It comes in the description of the motion of the particle diffusing in the medium, this is a rather traditional point of view for probability theory; but it also comes in the very description of the medium in which the diffusion takes place. The mathematical appeal of the subject stems from the fact that making the environment random has far reaching consequences, and simply stated models display unforeseen behaviors which represent mathematical challenges.