Gaussian mixtures: entropy and geometric inequalities
- Alexandros Eskenazis, P. Nayar, T. Tkocz
- MathematicsAnnals of Probability
- 15 November 2016
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.
A note on suprema of canonical processes based on random variables with regular moments
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…
A reverse entropy power inequality for log-concave random vectors
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…
Concentration inequalities and geometry of convex bodies
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…
Improved bounds for Hadwiger’s covering problem via thin-shell estimates
- Han Huang, Boaz A. Slomka, T. Tkocz, Beatrice-Helen Vritsiou
- MathematicsJournal of the European Mathematical Society…
- 30 November 2018
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…
A note on a Brunn-Minkowski inequality for the Gaussian measure
We give the counter-examples related to a Gaussian Brunn- Minkowski inequality and the (B) conjecture.
Tensor Products of Random Unitary Matrices
- T. Tkocz, Marek Smaczynski, M. Kuś, O. Zeitouni, K. Życzkowski
- Mathematics
- 16 March 2012
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…
On a convexity property of sections of the cross-polytope
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…
Reversal of Rényi Entropy Inequalities Under Log-Concavity
- J. Melbourne, T. Tkocz
- Computer ScienceIEEE Transactions on Information Theory
- 21 May 2020
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.
A randomly weighted minimum arborescence with a random cost constraint
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].
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