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

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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-Rényi entropy for p in the same range.

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Acknowledgments

We should very much like to thank Alexandros Eskenazis for the stimulating correspondence. We are also indebted to anonymous referees formany valuable comments which helped to significantly improve themanuscript.

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Authors and Affiliations

  1. Department of mathematics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Giorgos Chasapis, Keerthana Gurushankar & Tomasz Tkocz

Authors
  1. Giorgos Chasapis
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  2. Keerthana Gurushankar
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  3. Tomasz Tkocz
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Corresponding author

Correspondence to Tomasz Tkocz.

Additional information

TT’s research supported in part by NSF grant DMS-1955175.

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Chasapis, G., Gurushankar, K. & Tkocz, T. Sharp bounds on p-norms for sums of independent uniform random variables, 0 < p < 1. JAMA 149, 529–553 (2023). https://doi.org/10.1007/s11854-022-0256-x

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  • DOI: https://doi.org/10.1007/s11854-022-0256-x

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