52 citations · 130 across the 26 of their papers we have counts for
32 papers
Distributional stability of the Szarek and Ball inequalities
Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a fract…
Resilience of cube slicing in
Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
Ball's celebrated cube slicing (1986) asserts that among hyperplane sections of the cube in , the central section orthogonal to has the greatest vol…
Extremal sections and projections of certain convex bodies: a survey
Piotr Nayar, Tomasz Tkocz
We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly balls, by and onto lower dimensional subspaces. This s…
Log-concavity and discrete degrees of freedom
Jacek Jakimiuk, Daniel Murawski, Piotr Nayar +1
We develop the notion of discrete degrees of freedom of a log-concave sequence and use it to prove that geometric distribution minimises Rényi entropy of order infinity under fixed…
Rényi entropy and variance comparison for symmetric log-concave random variables
Maciej Białobrzeski, Piotr Nayar
We show that for any the Rényi entropy of order is minimized, among all symmetric log-concave random variables with fixed variance, either for a uniform distribution or f…
Slicing -balls reloaded: stability, planar sections in
Giorgos Chasapis, Piotr Nayar, Tomasz Tkocz
We show that the two-dimensional minimum-volume central section of the -dimensional cross-polytope is attained by the regular -gon. We establish stability-type results for h…