5 papers · 1 filter
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…
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…