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The Concentration of Measure Phenomenon by Michel Ledoux (Paperback, 2005)

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Product Information

The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. A familiar example is the way the uniform measure on the standard sphere $S^n$ becomes concentrated around the equator as the dimension gets large. This property may be interpreted in terms of functions on the sphere with small oscillations, an idea going back to Levy. The phenomenon also occurs in probability, as a version of the law of large numbers, due to Emil Borel. This book offers the basic techniques and examples of the concentration of measure phenomenon. The concentration of measure phenomenon was put forward in the early seventies by V. Milman in the asymptotic geometry of Banach spaces. It is of powerful interest in applications in various areas, such as geometry, functional analysis and infinite-dimensional integration, discrete mathematics and complexity theory, and probability theory.Particular emphasis is on geometric, functional, and probabilistic tools to reach and describe measure concentration in a number of settings. This book presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications, product measures, entropic and transportation methods, as well as aspects of M. Talagrand's deep investigation of concentration in product spaces and its application in discrete mathematics and probability theory, supremum of Gaussian and empirical processes, spin glass, random matrices, etc. Prerequisites are a basic background in measure theory, functional analysis, and probability theory.

Product Identifiers

PublisherAmerican Mathematical Society

ISBN-139780821837924

eBay Product ID (ePID)91883364

Product Key Features

Publication Year2005

SubjectMathematics

Number of Pages181 Pages

LanguageEnglish

Publication NameThe Concentration of Measure Phenomenon

TypeTextbook

AuthorMichel Ledoux

SeriesMathematical Surveys and Monographs

FormatPaperback

Additional Product Features

Country/Region of ManufactureUnited States

Title_AuthorMichel Ledoux