The parabolic Anderson model in a rough environment

SAMY TINDEL 

PURDUE UNIVERSITY

The parabolic Anderson model has to be interpreted as a heat equation in a random environment. In this talk I will first recall some basic physical and mathematical facts about this model. In particular, I will describe the so-called localization phenomenon for eigenvectors. 

In the second part of my talk I will focus on the description of the noisy Gaussian environment I’m interested in, especially in very rough (or singular) situations. I will then summarize the asymptotic behavior of moments obtained in the literature, including very recent results about critical cases.

If time allows it I will also give some hints about Feynman-Kac representations for the model, which are one of the the basic tools for its analysis.