Noam Berger: Random Walk in Random Environment

Lecture:
Wednesday 14:15-16:00 in the IRTG lounge, TU
starting on Wednesday, October 27.

Random walks on Z^d have been successfully studied since the beginning of the 20th century, and we have a highly detailed picture of their behavior. However, an examination of the methods shows that the perfect homogeneity of Z^d is crucial for almost all of the techniques used in the study of RW on Z^d. Since the 1970-s, an effort has been going on to try and understand random walks in inhomogeneous settings. The most studied such setting is that of a random environment, i.e. a random walk on Z^d, where the transition probabilities are determined in a random, translation invariant way. This model proved to be much more difficult than the classical RW, and many fundamental questions are still open.

In the course we will mostly consider systems in dimension greater than 1. We will start with the general theory, mostly due to Sznitman and Zerner, and then continue with the study of two specific types of systems: Random walks in reversible random environments and random walks in ballistic random environments. Special attention will be given to recent results and to open problems.

The only prerequisite is good knowledge of basic Probability Theory.