29/04/2026, 17:00 — 18:00 — Online
Francesco Caravenna, Università degli Studi di Milano-Bicocca
The 2D Stochastic Heat Equation in the strong disorder regime
We investigate the Stochastic Heat Equation (SHE) in the critical space dimension two, where it is ill-defined. A non-trivial solution, known as the critical 2D Stochastic Heat Flow (SHF), can be constructed through regularisation and renormalisation. We investigate the SHF in the strong-disorder regime, showing that it vanishes locally and identifying the spatial scale governing the transition from extinction to an averaged behavior. Corresponding results are established for the partition functions of 2D directed polymers, which shed light into the SHE regularised via space-time discretisation: when the disorder strength is kept fixed, the solution exhibits fluctuations on a superdiffusive scale. Based on joint works with Quentin Berger and Nicola Turchi.
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