Ofer Zeitouni: An introduction to limit laws for exit measures in random environment

Consider a large ball in \(\mathbb{Z}^d\); by exit measure we mean the distribution of the first point of the boundary hit by a random walk, or alternatively, the solution to the (discrete) Laplace equation. Now, perturb the generator of the random walk in an i.i.d. manner. This is the model of random walk in random environment. I will discuss some existing and conjectured results for the exit measure as the size of the ball grows. The talk will review some older results of Bolthausen and myself, some more recent work of Bolthausen and Bauer, and some work in progress.