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The concentration of measure phenomenon

Author: Michel Ledoux
Publisher: Providence, R.I. : American Mathematical Society, ©2001.
Series: Mathematical surveys and monographs, no. 89.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. This book offers the basic techniques and examples of the concentration of measure phenomenon. It  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michel Ledoux
ISBN: 0821828649 9780821828649 9780821837924 0821837923
OCLC Number: 47237544
Description: x, 181 pages ; 27 cm.
Contents: Concentration Functions and Inequalities --
Concentration functions --
Deviation inequalities --
Observable diameter --
Expansion coefficient --
Laplace bounds and infimum-convolutions --
Isoperimetric and Functional Examples --
Isoperimetric examples --
Brunn-Minkowski inequalities --
Semigroup tools --
Concentration and Geometry --
Spectrum and concentration --
Spectral and diameter bounds --
Levy families --
Topological applications --
Euclidean sections of convex bodies --
Concentration in Product Spaces --
Martingale methods --
Convex hull approximation --
Control by several points --
Convex infimum-convolution --
The exponential distribution --
Entropy and Concentration --
Logarithmic Sobolev inequalities and concentration --
Product measures --
Modified logarithmic Sobolev inequalities --
Discrete settings --
Covariance identities --
Transportation Cost Inequalities --
Information inequalities and concentration --
Quadratic transportation cost inequalities --
Transportation for product and non-product measures --
Sharp Bounds on Gaussian and Empirical Processes --
Gaussian processes --
Bounds on empirical processes --
Sharper bounds via the entropic method --
Selected Applications --
Concentration of harmonic measures --
Concentration for independent permutations --
Subsequences, percolation, assignment --
The spin glass free energy --
Concentration of random matrices.
Series Title: Mathematical surveys and monographs, no. 89.
Responsibility: Michel Ledoux.
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