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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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2023-04, Vol.149 (2), p.529-553
Main Authors: Chasapis, Giorgos, Gurushankar, Keerthana, Tkocz, Tomasz
Format: Article
Language:English
Subjects:
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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Summary: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