52 citations · 180 across the 41 of their papers we have counts for
8 papers · 1 filter
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…
Complex Hanner's Inequality for Many Functions
Jonathan Jenkins, Tomasz Tkocz
We establish Hanner's inequality for arbitrarily many functions in the setting where the Rademacher distribution is replaced with higher dimensional random vectors uniform on Eucli…
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…
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…
Injective Tauberian operators on and operators with dense range on
William B. Johnson, Amir Bahman Nasseri, Gideon Schechtman +1
There exist injective Tauberian operators on that have dense, non closed range. This gives injective, non surjective operators on that have dense range. Co…
On a Loomis-Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies
Piotr Nayar, Tomasz Tkocz
For a permutationally invariant unconditional convex body K in R^n we define a finite sequence (K_j), j = 1, ..., n of projections of the body K to the space spanned by first j vec…