Modul: MAT971 Seminar über stochastische Prozesse

## The critical 2d Stochastic Heat Flow

Talk by Prof. Dr. Francesco Caravenna

Speaker invited by: Prof. Dr. Jean Bertoin

**Date:** 01.03.23 **Time:** 17.15 - 18.45 **Room:** Y27H12

We consider the 2-dimensional Stochastic Heat Equation (SHE), which falls outside the scope of existing solution theories for singular stochastic PDEs. When we regularise the SHE by discretising space-time, the solution can be identified with 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 converges to a unique continuum limit: a universal process of random measures on R^2, which we call the critical 2d Stochastic Heat Flow. We investigate its features, showing in particular that it cannot be the exponential of a generalised Gaussian field.

Based on joint work with R. Sun and N. Zygouras.