P. Nayar

activity

20112023

most citedGaussian mixtures: entropy and geometric inequalities

52 citations · 130 across the 26 of their papers we have counts for

collaborators

Showing 2021Show all

4 papers · 1 filter

cs.IT2021★ 1 cited

Rényi entropy and variance comparison for symmetric log-concave random variables

Maciej Białobrzeski, Piotr Nayar

We show that for any $α > 0$ the Rényi entropy of order $α$ is minimized, among all symmetric log-concave random variables with fixed variance, either for a uniform distribution or f…

math.FA2021★ 12 cited

Slicing $ℓ_{p}$ -balls reloaded: stability, planar sections in $ℓ_{1}$

Giorgos Chasapis, Piotr Nayar, Tomasz Tkocz

We show that the two-dimensional minimum-volume central section of the $n$ -dimensional cross-polytope is attained by the regular $2 n$ -gon. We establish stability-type results for h…

math.MG2021

Reverse isoperimetric inequalities for parallel sets

Piotr Nayar

We consider the family of $r$ -parallel sets in $R^{d}$ , that is sets of the form $A_{r} = A + r B_{2}^{n}$ , where $B_{2}^{n}$ is the unit Euclidean ball and $A$ is an arbitrary Borel set.…

math.PR2021★ 9 cited

Khinchin-type inequalities via Hadamard's factorisation

Alex Havrilla, Piotr Nayar, Tomasz Tkocz

We prove Khinchin-type inequalities with sharp constants for type L random variables and all even moments. Our main tool is Hadamard's factorisation theorem from complex analysis,…

Rényi entropy and variance comparison for symmetric log-concave random variables

Slicing ℓp​-balls reloaded: stability, planar sections in ℓ1​

Reverse isoperimetric inequalities for parallel sets

Khinchin-type inequalities via Hadamard's factorisation

Slicing $ℓ_{p}$ -balls reloaded: stability, planar sections in $ℓ_{1}$