52 citations · 130 across the 26 of their papers we have counts for
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math.FA2022★ 3 cited
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…
math.FA2022★ 11 cited
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…
math.PR2022★ 1 cited
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…