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

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.

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Veröffentlicht in:	Journal d'analyse mathématique (Jerusalem) 2023-04, Vol.149 (2), p.529-553
Hauptverfasser:	Chasapis, Giorgos, Gurushankar, Keerthana, Tkocz, Tomasz
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Analysis Dynamical Systems and Ergodic Theory Entropy (Information theory) Functional Analysis Independent variables Lower bounds Mathematics Mathematics and Statistics Norms Partial Differential Equations Random variables
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Beschreibung
Zusammenfassung:	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.
ISSN:	0021-7670 1565-8538
DOI:	10.1007/s11854-022-0256-x