Nicola Turchi

activity

20172021

collaborators

6 papers

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.PR2019

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

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…