A Gaussian small deviation inequality for convex functions

DOI10.1214/17-AOP1206zbMath1429.60022arXiv1611.01723OpenAlexW2963880283MaRDI QIDQ1647733

Grigoris Paouris, Petros Valettas

Publication date: 26 June 2018

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.01723

zbMATH Keywords

small ball probabilityJohnson-Lindenstrauss lemmaconcentration for convex functionsEhrhard's inequality

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Asymptotic theory of convex bodies (52A23)

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Cites Work

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• Sharp comparison of moments and the log-concave moment problem
• Two observations regarding embedding subsets of Euclidean spaces in normed spaces
• Small ball probability and Dvoretzky's Theorem
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• An inequality for the multivariate normal distribution
• The Brunn-Minkowski inequality in Gauss space
• Averages of norms and quasi-norms
• The Ehrhard inequality
• Dichotomies, structure, and concentration in normed spaces
• On Dvoretzky's theorem for subspaces of \(L_p\)
• The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems
• The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite
• Random version of Dvoretzky's theorem in \(\ell_p^n\)
• A note on a Brunn-Minkowski inequality for the Gaussian measure
• Superconcentration and Related Topics
• Extensions of Lipschitz mappings into a Hilbert space
• Symétrisation dans l'espace de Gauss.
• Hessian of Bellman functions and uniqueness of the Brascamp–Lieb inequality
• Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
• On a quantitative reversal of Alexandrov’s inequality
• Small ball probability estimates in terms of width
• A note on the Ehrhard inequality
• The Random Version of Dvoretzky's Theorem in $l_{\infty}^n$

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