The critical 2d stochastic heat flow

16.11.2021 16:45 - 17:45

Nikos Zygouras (University of Warwick) (online)

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 methods used to tackle this problem is a blend of coarse graning techniques, Lindeberg principle, renewal theory and estimates around Schrodinger operators with point interactions and I ‘ll try to give a flavour of how all these are combined together.

Based on a joint work with Francesco Caravenna and Rongfeng Sun

Organiser:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Location:

HS 5, EG., OMP 1