"Motion in random media"
Abstract: Classical random walks have been studied for
many decades, and by now detailed knowledge exists on almost every
aspect of them. Not surprisingly, most of the methods for studying
them are based on the regularity and group structure of the medium,
as well as the Markovian behavior of the walk. However, when
attempting to use random walk as a model for physical processes,
both the assumption of regularity and that of Markovian behavior are
no longer valid. Therefore in the last three decades a significant
research effort has been directed towards models of random walks that
do not satisfy these assumptions. One of the most important of these
models is that of random walk in random environment (RWRE). In the
talk I will describe RWRE, compare its behavior to that of classical
random walk and present a few predictable as well as a few
surprising results. I will conclude with some open problems.