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

Giorgos Chasapis; Keerthana Gurushankar; Tomasz Tkocz

doi:10.1007/s11854-022-0256-x

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arXiv · 2105.14079

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

Giorgos Chasapis·Keerthana Gurushankar·Tomasz Tkocz

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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 $p$-R\'enyi entropy for $p$ in the same range.

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Giorgos Chasapis, Keerthana Gurushankar, Tomasz Tkocz. 2021-05-28. Sharp bounds on $p$-norms for sums of independent uniform random variables, $0 < p < 1$. https://doi.org/10.1007/s11854-022-0256-x

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