9 citations · 21 across the 11 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…