A simple proof of the majorizing measure theorem
type: Item
instance of: scholarly article
title: A simple proof of the majorizing measure theorem
zbMATH Open document ID: 0760.60043
DOI: 10.1007/BF01895708
author: Michel Talagrand
published in: Geometric and Functional Analysis. GAFA
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/58140
review text: Let \(X=\{X_ t; t\in T\}\) be a centered Gaussian process with a parameter set \(T\) equipped with and bounded in the canonical metric \(d\). The author [Acta Math. 159, No. 1-2, 99-149 (1987; Zbl 0712.60044)] proved that if \(X\) is bounded with probability one, then there exists a probability measure \(m\) on \((T,d)\) such that for some universal constant \(K\) \[ \sup_{t\in T}\int_ 0^{\infty}\sqrt{\log (1/m(\{s\in T: d(s,t)\leq \epsilon\}))} d\epsilon \leq K E\sup_{t\in T}X_ t. \] The first proof of this statement was quite difficult and was based on properties of ultrametric spaces. In the paper under review a new proof is given. Now the proof relies upon Sudakov's minoration, the concentration of measure phenomenon, and a simple construction.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 56875
zbMATH Keywords: properties of ultrametric spaces
zbMATH Keywords: Sudakov's minoration
zbMATH Keywords: concentration of measure phenomenon
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
cites work: Q3997990
cites work: Regularity of Gaussian processes
cites work: Q4037241
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description: scientific article; zbMATH DE number 56875