Pointwise statistics of 2D stochastic heat equations

The stochastic heat equation is a fundamental model in statistical physics featuring noise scaled by the solution itself. In this talk, I will discuss the pointwise statistics of a family of nonlinear stochastic heat equations in the critical dimension two. Curiously, these statistics evoke a "forward-backward" SDE and a quasilinear but deterministic heat equation. The well-posedness of the latter is delicate and consequential.

This is joint work with Alexander Dunlap.