7 papers
The Critical 2d Stochastic Heat Flow and Related Models
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
In these lecture notes, we review recent progress in the study of the stochastic heat equation and its discrete analogue, the directed polymer model, in spatial dimension 2. It was…
Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers
Quentin Berger, Francesco Caravenna, Nicola Turchi
The critical 2D Stochastic Heat Flow (SHF) is a universal measure-valued process that provides a notion of solution to the ill-defined 2D stochastic heat equation. We investigate t…
From disordered systems to the Critical 2D Stochastic Heat Flow
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
We review our joint work on the scaling limits of disordered systems, linking the notion of disorder relevance/irrelevance to that of sub/super-criticality of singular SPDEs. This…
Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow
Francesco Caravenna, Anna Donadini
We investigate noise sensitivity beyond the classical setting of binary random variables, extending the celebrated result by Benjamini, Kalai, and Schramm to a wide class of functi…
Singularity and regularity of the critical 2D Stochastic Heat Flow
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
The Critical 2D Stochastic Heat Flow (SHF) provides a natural candidate solution to the ill-posed 2D Stochastic Heat Equation with multiplicative space-time white noise. In this pa…
Quasi-critical fluctuations for 2d directed polymers
Francesco Caravenna, Francesca Cottini, Maurizia Rossi
We study the 2d directed polymer in random environment in a novel *quasi-critical regime*, which interpolates between the much studied sub-critical and critical regimes. We prove E…