9 citations · 21 across the 11 of their papers we have counts for
14 papers
On random diameters of convex bodies
O. Guedon, A. E. Litvak, K. Tatarko +1
Let be a convex body containing the origin in its interior. In this work, we study the diameters of random sections of and derive upper and lower bound…
Illuminating 1-unconditional convex bodies in and , 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 and in . Moreover, we settle the conjecture for th…
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…
A Bootstrap Algorithm for Fast Supervised Learning
Michael A Kouritzin, Stephen Styles, Beatrice-Helen Vritsiou
Training a neural network (NN) typically relies on some type of curve-following method, such as gradient descent (GD) (and stochastic gradient descent (SGD)), ADADELTA, ADAM or lim…
Regular ellipsoids and a Blaschke-Santaló-type inequality for projections of non-symmetric convex bodies
Beatrice-Helen Vritsiou
It is shown that every not-necessarily symmetric convex body in has an affine image of such that the covering numbers of by growing…
A note on volume thresholds for random polytopes
Debsoumya Chakraborti, Tomasz Tkocz, Beatrice-Helen Vritsiou
We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-c…
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 are obtained in the high-dimensional regime, that is, as . In particular,…
Improved bounds for Hadwiger's covering problem via thin-shell estimates
Han Huang, Boaz A. Slomka, Tomasz Tkocz +1
A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number is such that every convex body in ${\mathbb R}…
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…
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…
Geometry of the -centroid bodies of an isotropic log-concave measure
Apostolos Giannopoulos, Pantelis Stavrakakis, Antonis Tsolomitis +1
We study some geometric properties of the -centroid bodies of an isotropic log-concave measure on . For any $2\ls q\ls\sqrt{n}$ and for $\varepsilo…
Further unifying two approaches to the hyperplane conjecture
Beatrice-Helen Vritsiou
We compare and combine two approaches that have been recently introduced by Dafnis and Paouris [DP] and by Klartag and Milman [KM] with the aim of providing bounds for the isotropi…
The isotropic position and the reverse Santaló inequality
Apostolos Giannopoulos, Grigoris Paouris, Beatrice-Helen Vritsiou
We present proofs of the reverse Santaló inequality, the existence of M-ellipsoids and the reverse Brunn-Minkowski inequality, using purely convex geometric tools. Our approach is…
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…