141 citations · 238 across the 33 of their papers we have counts for
5 papers · 1 filter
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…
On generic chaining and the smallest singular value of random matrices with heavy tails
Shahar Mendelson, Grigoris Paouris
We present a very general chaining method which allows one to control the supremum of the empirical process $\sup_{h \in H} |N^{-1}\sum_{i=1}^N h^2(X_i)-\E h^2|$ in rather general…
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…
On the approximation of a polytope by its dual -centroid bodies
Grigoris Paouris, Elisabeth M. Werner
We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid bodies is independent of the geometry of P.…
Isomorphic properties of Intersection bodies
A. Koldobsky, G. Paouris, M. Zymonopoulou
We study isomorphic properties of two generalizations of intersection bodies, the class of k-intersection bodies and the class of generalized k-intersection bodies. We also show th…