Nonlinear weak-noise stochastic heat equations in two dimensions

Abstract: I will discuss a two-dimensional stochastic heat equation in the weak noise regime with a nonlinear noise strength. I will explain how pointwise statistics of solutions to this equation, as the correlation length of the noise is taken to 0 but the noise is attenuated by a logarithmic factor, can be related to a forward-backward stochastic differential equation (FBSDE) depending on the nonlinearity. I will also discuss two cases in which the FBSDE can be explicitly solved: the linear stochastic heat equation, for which we recover the log-normal behavior proved by Caravenna, Sun, and Zygouras, and branching Brownian motion/super-Brownian motion, for which we obtain a solution to the Feller diffusion. This talk will be based on joint work with Yu Gu and with Cole Graham.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .