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Concentration of measure and isoperimetric inequalities in product spaces
 Michel Talagrand
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The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product Ω^{N} of probability spaces has measure at least one half, “most” of the points of Ωn are “close” to A. We proceed to a systematic exploration of this phenomenon. The meaning of the word “most” is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work “close” is defined in three main ways, each of them giving rise to related, but different inequalities. The inequalities are all proved through a common scheme of proof. Remarkably, this simple approach not only yields qualitatively optimal results, but, in many cases, captures near optimal numerical constants. A large number of applications are given, in particular to Percolation, Geometric Probability, Probability in Banach Spaces, to demonstrate in concrete situations the extremely wide range of application of the abstract tools.
Dedicated to Vitali Milman
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 Title
 Concentration of measure and isoperimetric inequalities in product spaces
 Journal

Publications Mathématiques de l'Institut des Hautes Études Scientifiques
Volume 81, Issue 1 , pp 73205
 Cover Date
 19951201
 DOI
 10.1007/BF02699376
 Print ISSN
 00738301
 Online ISSN
 16181913
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Primary 60E15, 28A35, 60G99
 Secondary 60G15, 68C15
 Authors

 Michel Talagrand ^{(1)}
 Author Affiliations

 1. Equipe d’Analyse  Tour 48 UA au CNRS no 754, Université Paris VI, 4 Pl. Jussieu, 75230, Paris Cedex 05