52 citations · 180 across the 41 of their papers we have counts for
9 papers · 1 filter
Improved bounds for Hadwiger's covering problem via thin-shell estimates
Han Huang, Boaz A. Slomka, Tomasz Tkocz +1
A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number is such that every convex body in ${\mathbb R}…
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…
On the cover time of the emerging giant
Alan Frieze, Wesley Pegden, Tomasz Tkocz
Let . It is known that if then w.h.p. has a unique giant largest component. We show that if in addition, $\varepsil…
Comparison of moments of Rademacher chaoses
Paata Ivanisvili, Tomasz Tkocz
We show that complex hypercontractivity gives better constants than real hypercontractivity in comparison inequalities for (low) moments of Rademacher chaoses (homogeneous polynomi…
A note on log-concave random graphs
Alan Frieze, Tomasz Tkocz
We establish a threshold for the connectivity of certain random graphs whose (dependent) edges are determined by the uniform distributions on generalized Orlicz balls, crucially us…
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…
Stochastic dominance and weak concentration for sums of independent symmetric random vectors
Witold Bednorz, Tomasz Tkocz
Kwapien and Woyczynski asked in their monograph (1992) whether their notion of superstrong domination is inherited when taking sums of independent symmetric random vectors (one vec…
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…