5 papers
Fractional moments of the Stochastic Heat Flow and 2D Directed Polymers
Quentin Berger, Nicola Turchi, Nikos Zygouras
We estimate the fractional moments of the normalized mass assigned by the Critical 2D Stochastic Heat Flow to small balls. Our results also cover the discrete case corresponding to…
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…
On the moments of the mass of shrinking balls under the Critical Stochastic Heat Flow
Ziyang Liu, Nikos Zygouras
The Critical Stochastic Heat Flow (SHF) is a measure valued stochastic process on that defines a non-trivial solution to the two-dimensional stochastic heat equ…
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…
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…