52 citations · 130 across the 26 of their papers we have counts for
4 papers · 1 filter
Sharp moment-entropy inequalities and capacity bounds for log-concave distributions
Mokshay Madiman, Piotr Nayar, Tomasz Tkocz
We show that the uniform distribution minimizes entropy among all one-dimensional symmetric log-concave distributions with fixed variance, as well as various generalizations of thi…
On a convexity property of sections of the cross-polytope
Piotr Nayar, Tomasz Tkocz
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…
Bounds on moments of weighted sums of finite Riesz products
Aline Bonami, Rafał Latała, Piotr Nayar +1
Let be a lacunary sequence of integers, such that . We are interested in linear combinations of the sequence of finite Riesz products $\prod_{j=1}^N(1+\cos…
Sharp comparison of moments and the log-concave moment problem
Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal co…