A correlation inequality for symmetric geodesically convex sets in the unit sphere equipped with the normalized surface area measure is obtained and sharp constants in Khintchine inequalities for vectors uniformly distributed on the unit balls with respect to $p-norms are derived.Expand

We derive two-sided bounds for expected values of suprema of canonical processes based on random variables with moments growing regularly. We also discuss a Sudakov-type minoration principle for… Expand

We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy power inequalities… Expand

Our goal is to write an extended version of the notes of a course given by Olivier Gu edon at the Polish Academy of Sciences from April 11-15, 2011. The course is devoted to the study of… Expand

A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N\left(n\right)$ is such that every convex body in ${\mathbb R}^{n}$ can be… Expand

Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes… Expand

We establish the log-concavity of the volume of central sections of dilations of the cross-polytope (the strong B-inequality for the cross-polytope and Lebesgue measure restricted to an arbitrary… Expand

A discrete analog of the Rényi entropy comparison due to Bobkov and Madiman is established, and the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis is investigated.Expand

The asymptotic value of the optimum weight via the consideration of a dual problem is established, for a range of values for [Formula: see text].Expand