The nonlinear stochastic heat equation in the critical dimension


Event details

Date 21.03.2023
Hour 15:0015:50
Speaker Alexander Dunlap (Courant Institute)
Category Conferences - Seminars
Event Language English

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.


Practical information

  • General public
  • Free



Probability and Stochastic Analysis Seminar

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