# Moment Estimates for some Renormalized Parabolic Anderson Models

## When:

Nov 11, 2019 - 1:50pm to 2:55pm

## Where:

Siegal Hall, Room 118

## Speaker:

Samy Tindel
Department of Mathematics, Purdue University

## Description:

In this talk I will first introduce and recall some basic facts about the parabolic Anderson model. This model can simply be seen as a linear heat equation in a random environment. I will spend some time describing a couple of manifestations of what is usually called localization, which is the main physical phenomenon observed in this context. Then I will talk about some recent developments concerning parabolic Anderson models in a very rough environment (namely a noise with very singular space-time covariance function). The theory of regularity structures enables the definition parabolic Anderson models in rough contexts. If we call $$u(t,x)$$ the solution to our renormalized stochastic heat equation, I will give some information about the moments of $$u(t,x)$$ when the stochastic heat equation is interpreted in the Skorohod as well as in the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.

## Event Type:

Department of Applied Mathematics - Colloquia