A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences

zbMath1159.05054arXiv0804.1181MaRDI QIDQ1010896

Leonid Gurvits

Publication date: 7 April 2009

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1181

zbMATH Keywords

Minkowski sumMinkowski polynomialconvolution of ultra-logconcave sequencesmixed volumes of convex sets

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Other problems of combinatorial convexity (52A37)

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Concentration inequalities for ultra log-concave distributions ⋮ Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measures ⋮ Khinchine type inequalities with optimal constants via ultra log-concavity ⋮ Log-Hessian and deviation bounds for Markov semi-groups, and regularization effect in \(\mathbb{L}^1 \) ⋮ Log-concavity and strong log-concavity: a review ⋮ A strong log-concavity property for measures on Boolean algebras ⋮ On an exponential functional for Gaussian processes and its geometric foundations ⋮ Strong Log-concavity is Preserved by Convolution

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