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

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

Probability 2025-01-28 v3

Authors: Giorgos Chasapis , Keerthana Gurushankar , Tomasz Tkocz

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

p-norm independent uniform random variables variance sharp lower bound p-Rényi entropy probability inequalities

Cite

@article{arxiv.2105.14079,
  title  = {Sharp bounds on $p$-norms for sums of independent uniform random variables, $0 < p < 1$},
  author = {Giorgos Chasapis and Keerthana Gurushankar and Tomasz Tkocz},
  journal= {arXiv preprint arXiv:2105.14079},
  year   = {2025}
}

Comments

20 pages, 2 figures. Final version, to appear in Journal d'Analyse Math\'ematique

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

Abstract

Keywords

Cite

Comments

Related papers