Research-The Parabolic Anderson Model and Negative Curvature

Research

Probability & Statistics Seminar

The Parabolic Anderson Model and Negative Curvature

Speaker: Hongyi CHEN（University of Illinois Chicago）
Time: Dec 17, 2024, 16:00-17:00
Location: Room M3009, College of Science Building

Abstract

We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in space parameterized by a regularity parameter $\alpha$, which we use to explore regularity requirements for well-posedness. Then, we show that conditions on the heat kernel imply an exponential in time upper bound for the moments of the solution, and a lower bound for sectional curvature imply a corresponding lower bound. These results hold if the noise is strong enough, where the needed strength of the noise is affected by sectional curvature. （This will be a blackboard talk.）