Nikolaos Zygouras

The critical 2d stochastic heat flow

We consider directed polymers in random environment in the critical dimension two, focusing on the intermediate disorder regime when the model undergoes a phase transition. We prove that, at the critical temperature the diffusively rescaled random field of partition functions has a unique scaling limit ; a universal process of random measures on R^2 with logarithmic correlations, which we call the Critical 2d Stochastic Heat Flow. This is the natural candidate for the long sought solution of the critical 2d Stochastic Heat Equation with multiplicative space-time white noise. The construction of the Critical 2d Stochastic Heat Flow opens a number of questions and links to other topics, which I discuss. Based on a joint work with Francesco Caravenna and Rongfeng Sun