Some deviation inequalities
type: Item
instance of: scholarly article
title: Some deviation inequalities
zbMATH Open document ID: 0756.60018
DOI: 10.1007/BF01896377
published in: Geometric and Functional Analysis. GAFA
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9201216
full work available at URL: https://eudml.org/doc/58114
review text: The author gives short proofs of a deviation inequality of Talagrand and of some concentration results for Gaussian measures as e.g. Pisier's inequality, \(E\exp{\lambda \over \sqrt{2}}(\varphi(X)-\varphi(Y))\leq e^{\lambda^ 2/2}\) for all real \(\lambda\) and independent Gaussian vectors with independent components and Lipschitzian's \(\varphi\). The proofs are based on stability properties of the ``property \((\tau)\)'' of a pair \((\mu,w)\) defined by the class of inequalities \((\int e^{\varphi\square w}d\mu)(\int e^{-\varphi}d\mu)\leq 1\) for all bounded \(\varphi\); \(\varphi\square w\) denoting the infimal convolution on \(\mathbb{R}^ n\).
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 56878
zbMATH Keywords: concentration results for Gaussian measures
zbMATH Keywords: Pisier's inequality
zbMATH Keywords: stability properties
Wikidata QID: Q93439211
author: Bernard Maurey
MaRDI profile type: Publication
arXiv ID: math/9201216
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OpenAlex ID: W2096324813
description: scientific article