Beatrice-Helen Vritsiou

activity

20112019

collaborators

6 papers

math.MG2024

Illuminating 1-unconditional convex bodies in $R^{3}$ and $R^{4}$ , and certain cases in higher dimensions

Wen Rui Sun, Beatrice-Helen Vritsiou

We settle the Hadwiger-Boltyanski Illumination Conjecture for all 1-unconditional convex bodies in $R^{3}$ and in $R^{4}$ . Moreover, we settle the conjecture for th…

math.MG2024

On the illumination of 1-symmetric convex bodies

Wen Rui Sun, Beatrice-Helen Vritsiou

In ["Illumination of convex bodies with many symmetries", Mathematika 63 (2017)], Tikhomirov verified the Hadwiger-Boltyanski Illumination Conjecture for the class of 1-symmetric c…

math.MG2019

Asymptotic normality for random simplices and convex bodies in high dimensions

David Alonso-Gutiérrez, Florian Besau, Julian Grote +5

Central limit theorems for the log-volume of a class of random convex bodies in $R^{n}$ are obtained in the high-dimensional regime, that is, as $n \to \infty$ . In particular,…

math.FA2018

Selberg-type integrals and the variance conjecture for the operator norm

Beatrice-Helen Vritsiou

The variance conjecture in Asymptotic Convex Geometry stipulates that the Euclidean norm of a random vector uniformly distributed in a (properly normalised) high-dimensional convex…

math.FA2016

On the thin-shell conjecture for the Schatten classes

Jordan Radke, Beatrice-Helen Vritsiou

We study the thin-shell conjecture for the Schatten classes. In particular, we establish the conjecture for the operator norm; we also improve on the best known bound for the Schat…

math.FA2011

A remark on the slicing problem

Apostolos Giannopoulos, Grigoris Paouris, Beatrice-Helen Vritsiou

The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I_1(K,Z_q^o(K))=\int_K ||< :, x> ||_{L_q(K)}dx. We show that an upper bo…