Alex Dunlap (NYU)


Wednesday April 5, 2023
12:00 pm - 1:00 pm


Jeffery Hall, Room 319

Probability Seminar

Wednesday, April 5th, 2023

Time: 12:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Alex Dunlap (NYU)

Title: The nonlinear stochastic heat equation in the critical dimension

Abstract: I will discuss a two-dimensional stochastic heat equation with a nonlinear noise strength, and consider a limit in which the correlation length of the noise is taken to 0 but the noise is attenuated by a logarithmic factor. The limiting pointwise statistics can be related to a stochastic differential equation in which the diffusivity solves a PDE somewhat reminiscent of the porous medium equation. This relationship is established through the theory of forward-backward SDEs. I will also explain several cases in which the PDE can be solved explicitly, some of which correspond to known probabilistic models. This talk will be based on current joint work with Cole Graham and earlier joint work with Yu Gu.