January 19, 2001

NOTE: SEMINAR BEGINS AT 12:00 NOON
BLDG 380 ROOM 383-N

Marek Biskup
Theory Group, Microsoft Research

Long-time tails for diffusions in random media:
parabolic Anderson model with bounded potentials

Abstract

I will discuss the long-time asymptotics (both of the moments and almost sure) of the solution to a parabolic second-order differential problem (so called parabolic Anderson model) on the d dimensional integer lattice with a random i.i.d. potential, bounded from above. Both asymptotics are determined by appropriate variational principles. As an application, the Lifshitz tails for the spectrum of the associated random Schroedinger operator (Anderson Hamiltonian) can explicitly be computed. The results extend various findings about the "simple random walk among Poissonian obstacles" obtained by Sznitman and his school in the 1990s.

This is a joint work with Wolfgang Koenig, based on two papers that can be retrieved on the web from http://research.microsoft.com/users/biskup/papers.htm

Seminar Main Page