141 citations · 238 across the 33 of their papers we have counts for
14 papers · 1 filter
Measure comparison and distance inequalities for convex bodies
Alexander Koldobsky, Grigoris Paouris, Artem Zvavitch
We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We al…
Hypercontractivity and Lower Deviation Estimates in Normed Spaces
Grigoris Paouris, Konstantin Tikhomirov, Petros Valettas
We consider the problem of estimating small ball probabilities for sub-additive,positively homogeneous functions with respect to th…
Dichotomies, structure, and concentration in normed spaces
Grigoris Paouris, Petros Valettas
We use probabilistic, topological and combinatorial methods to establish the following deviation inequality: For any normed space there exists an inve…
Variance estimates and almost Euclidean structure
Grigoris Paouris, Petros Valettas
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on , which provide sharp distributional inequalities. In the…
Generalized Dual Sudakov Minoration via Dimension Reduction - A Program
Shahar Mendelson, Emanuel Milman, Grigoris Paouris
We propose a program for establishing a conjectural extension to the class of (origin-symmetric) log-concave probability measures , of the classical dual Sudakov Minoration on t…
On Dvoretzky's theorem for subspaces of
Grigoris Paouris, Petros Valettas
We prove that for any and for every -dimensional subspace of , represented on , whose unit ball is in Lewis' position one has the follow…