6 papers · 1 filter
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…
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…
The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices
Giovanni Peccati, Nicola Turchi
We compute quantitative bounds for measuring the discrepancy between the distribution of two min-max statistics involving either pairs of Gaussian random matrices, or one Gaussian…
Phase transition for the volume of high-dimensional random polytopes
Gilles Bonnet, Zakhar Kabluchko, Nicola Turchi
The beta polytope is the convex hull of i.i.d. random points distributed in the unit ball of according to a density proportional to $(1-\lVert{x}\rVe…
Geometry of -balls: Classical results and recent developments
Joscha Prochno, Christoph Thäle, Nicola Turchi
This survey will appear as a chapter in the forthcoming "Proceedings of the HDP VIII Conference".
Limit theorems for random polytopes with vertices on convex surfaces
Nicola Turchi, Florian Wespi
The random polytope , defined as the convex hull of points chosen uniformly at random on the boundary of a smooth convex body, is considered. Proofs for lower and upper va…