Nicola Turchi

activity

20172026

most citedThreshold phenomena for high-dimensional random polytopes

17 citations · 30 across the 11 of their papers we have counts for

collaborators

12 papers

math.PR2026

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…

math.PR2025

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.MG2024

Weighted floating functions and weighted functional affine surface areas

Carsten Schütt, Christoph Thaele, Nicola Turchi +1

The purpose of this paper is to introduce the new concept of weighted floating functions associated with log concave or $s$ -concave functions. This leads to new notions of weighted…

math.PR2021

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…

math.ST2021★ 2 cited

Nonparametric needlet estimation for partial derivatives of a probability density function on the $d$ -torus

Claudio Durastanti, Nicola Turchi

This paper is concerned with the estimation of the partial derivatives of a probability density function of directional data on the $d$ -dimensional torus within the local threshold…

math.PR2019★ 10 cited

Phase transition for the volume of high-dimensional random polytopes

Gilles Bonnet, Zakhar Kabluchko, Nicola Turchi

The beta polytope $P_{n, d}^{β}$ is the convex hull of $n$ i.i.d. random points distributed in the unit ball of $R^{d}$ according to a density proportional to $(1-\lVert{x}\rVe…

math.PR2018

Geometry of $ℓ_{p}^{n}$ -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".

math.MG2018

The isotropic constant of random polytopes with vertices on convex surfaces

Joscha Prochno, Christoph Thäle, Nicola Turchi

For an isotropic convex body $K \subset R^{n}$ we consider the isotropic constant $L_{K_{N}}$ of the symmetric random polytope $K_{N}$ generated by $N$ independent random points w…

math.MG2018★ 17 cited

Threshold phenomena for high-dimensional random polytopes

Gilles Bonnet, Giorgos Chasapis, Julian Grote +2

Let $X_{1}, \dots, X_{N}$ , $N > n$ , be independent random points in $R^{n}$ , distributed according to the so-called beta or beta-prime distribution, respectively. We establish thre…

math.PR2017

Limit theorems for random polytopes with vertices on convex surfaces

Nicola Turchi, Florian Wespi

The random polytope $K_{n}$ , defined as the convex hull of $n$ points chosen uniformly at random on the boundary of a smooth convex body, is considered. Proofs for lower and upper va…

math.MG2017★ 1 cited

Monotonicity of facet numbers of random convex hulls

Gilles Bonnet, Julian Grote, Daniel Temesvari +3

Let $X_{1}, \dots, X_{n}$ be independent random points that are distributed according to a probability measure on $R^{d}$ and let $P_{n}$ be the random convex hull generated by $X_…

math.MG2017

Random polytopes: central limit theorems for intrinsic volumes

Christoph Thaele, Nicola Turchi, Florian Wespi

Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimat…