Sharp bounds on $p$-norms for sums of independent uniform random variables, $0<p<1$

Abstract

We provide a sharp lower bound on the $p$-norm of a sum of independent uniform random variables in terms of its variance when $0<p<1$. We address an analogous question for $p$-Rényi entropy for $p$ in the same range.

20 pages, 2 figures. Final version, to appear in Journal d'Analyse Mathématique

References in corpus (1)

• Khinchin-type inequalities via Hadamard's factorisation

Cited by in corpus (2)

• Distributional stability of the Szarek and Ball inequalities
• Haagerup's phase transition at polydisc slicing