Abstract

The two-dimensional stochastic heat equation (SHE) at criticality was introduced in the ’90s. It arises from problems of statistical physics through several models of stochastic surface growth dynamics and the disordered system of a directed polymer in a random medium. Nevertheless, the equation has been known to pose difficulties to solution theories of stochastic partial differential equations despite the “trivial” form that the equation takes.

This talk will provide an overview of stochastic analytic descriptions of the twodimensional SHE at criticality. Such descriptions for the discussion include the Feynman-Kac-type formulas for the moments and extend to the pathwise level by the martingale characterization of the solutions.

 

Organizer: Yuan-Chung Sheu (NYCU)