Seminar

Intermittency usually refers to something occurring irregularly at different scales or tall peaks on small regions, typically as time gets larger.

In the first part of this talk, instead of looking at a large time behavior, we will consider nonlinear noise excitation of a large family of intermittent stochastic partial differential equations (SPDEs). We show that there is a near-dichotomy: “Semi-discrete” equations are nearly always far less excitable than “continuous” equations.

In the second part of this talk, we consider large scale structures of points of tall peaks for various SPDEs such as parabolic Anderson models (which are intermittent) and SPDEs with additive noise (which are not intermittent). We show that parabolic Anderson models are multi-fractal (as expected), but so are SPDEs with additive noise.

This is based on joint works with Davar Khoshnevisan and Yimin Xiao.