Khinchine type inequalities with optimal constants via ultra log-concavity

DOI10.1007/s11117-011-0130-zzbMath1260.60031OpenAlexW2064144945MaRDI QIDQ1928539

Krzysztof Oleszkiewicz, Piotr Nayar

Publication date: 3 January 2013

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-011-0130-z

zbMATH Keywords

factorial momentslog-concavityKhinchine inequalityultra log-concavity

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Probability distributions: general theory (60E05) Inequalities for sums, series and integrals (26D15)

Related Items (15)

Sharp Khinchin-type inequalities for symmetric discrete uniform random variables ⋮ Log-concavity and log-convexity of moments of averages of i.i.d. random variables ⋮ Entropy-variance inequalities for discrete log-concave random variables via degree of freedom ⋮ Log-Hessian and deviation bounds for Markov semi-groups, and regularization effect in \(\mathbb{L}^1 \) ⋮ Sudakov minoration for products of radial-type log-concave measures ⋮ Geometric and functional inequalities for log-concave probability sequences ⋮ Sharp bounds on \(p\)-norms for sums of independent uniform random variables, \(0 < p < 1\) ⋮ Precise moment and tail bounds for Rademacher sums in terms of weak parameters ⋮ Log-concavity and strong log-concavity: a review ⋮ From Ball's cube slicing inequality to Khinchin-type inequalities for negative moments ⋮ Sharp comparison of moments and the log-concave moment problem ⋮ Random Graphs with a Fixed Maximum Degree ⋮ Gaussian mixtures: entropy and geometric inequalities ⋮ On the \(\ell_4:\ell_2\) ratio of functions with restricted Fourier support ⋮ Strong Log-concavity is Preserved by Convolution

Cites Work

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• Log-concavity and the maximum entropy property of the Poisson distribution
• A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences
• Ultra logconcave sequences and negative dependence
• Comparison of moments of sums of independent random variables and differential inequalities
• On the best constants in the Khinchin inequality
• The best constants in the Khintchine inequality
• Pólya sequences, binomial convolution and the union of random sets
• Majorization of sequences, sharp vector Khinchin inequalities, and bisubharmonic functions
• Properties of Probability Distributions with Monotone Hazard Rate
• Best Khintchine type inequalities for sums of independent, rotationally invariant random vectors

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