activity
20242026
collaborators

7 papers

math.PR2026

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…

math.PR2026

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…

math.PR2026

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…

math.PR2025

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…

math.PR2025

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…

math.PR2025

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…