Math Colloquia

The critical 2d Stochastic Heat Flow

by Prof. Francesco Caravenna (Milano Bicocca)

Rectorate/Building-Auditorium (GSSI)





(joint work with R. Sun and N. Zygouras)

We consider the 2d heat equation with multiplicative space-time white noise, known as the 2d Stochastic Heat Equation (SHE). This is a critical stochastic PDE which falls outside the scope of robust solution theories, such as Regularity Structures or Paracontrolled Calculus. When space-time is suitably discretised, the solution of the SHE can be interpreted as the partition function of a statistical mechanics model, the so-called directed polymer in random environment. We prove that as the discretisation is removed, and the noise strength is rescaled in a critical way, the solution of the discretised SHE converges to a unique limit: a universal process of random measures on R^2, which we call the critical 2d Stochastic Heat Flow. We investigate some of its features, getting explicit bounds on its moments, and we outline future directions of research.


The seminar will be held in the Main Auditorium and it will also be streamed online via zoom at this link:

Please notice that, in accordance to GSSI regulations, your Green Pass will be checked at the entrance.