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The concentration of measure phenomenon / Michel Ledoux.

By: Ledoux, Michel, 1958-.
Series: Mathematical surveys and monographs: no. 89.Publisher: Providence, R.I. : American Mathematical Society, c2001Description: x, 181 p. ; 27 cm.ISBN: 0821828649 (acidfree paper).Subject(s): Concentration functions | Measure theory | ProbabilitiesDDC classification: 519.2 Online resources: Full-text here
Contents:
Machine generated contents note: INTRODUCTION vii -- 1. CONCENTRATION FUNCTIONS -- AND INEQUALITIES 1 -- 1.1 First examples 1 -- 1.2 Concentration functions 3 -- 1.3 Deviation inequalities 5 -- 1.4 Observable diameter 14 -- 1.5 Expansion coefficient 15 -- 1.6 Laplace bounds and infimum-convolutions 16 -- Notes and Remarks 21 -- 2. ISOPERIMETRIC AND FUNCTIONAL EXAMPLES 23 -- 2.1 Isoperimetric examples 23 -- 2.2 Brunn-Minkowski inequalities 32 -- 2.3 Semigroup tools 38 -- Notes and Remarks 44 -- 3. CONCENTRATION AND GEOMETRY 47 -- 3.1 Spectrum and concentration 47 -- 3.2 Spectral and diameter bounds 53 -- 3.3 L6vy families 55 -- 3.4 Topological applications 57 -- 3.5 Euclidean sections of convex bodies 60 -- Notes and Remarks 65 -- 4. CONCENTRATION IN PRODUCT SPACES 67 -- 4.1 Martingale methods 67 -- 4.2 Convex hull approximation 72 -- 4.3 Control by several points 79 -- 4.4 Convex infimum-convolution 82 -- 4.5 The exponential distribution 83 -- Notes and Remarks 89 -- 5. ENTROPY AND CONCENTRATION 91 -- 5.1 Logarithmic Sobolev inequalities and concentration 91 -- 5.2 Product measures 97 -- 5.3 Modified logarithmic Sobolev inequalities 101 -- 5.4 Discrete settings 108 -- 5.5 Covariance identities 114 -- Notes and Remarks 115 -- 6. TRANSPORTATION COST INEQUALITIES 117 -- 6.1 Information inequalities and concentration 117 -- 6.2 Quadratic transportation cost inequalities 122 -- 6.3 Transportation for product and non-product measures 126 -- Notes and Remarks 132 -- 7. SHARP BOUNDS ON GAUSSIAN -- AND EMPIRICAL PROCESSES 133 -- 7.1 Gaussian processes 133 -- 7.2 Bounds on empirical processes 138 -- 7.3 Sharper bounds via the entropic method 142 -- Notes and Remarks 149 -- 8. SELECTED APPLICATIONS 151 -- 8.1 Concentration of harmonic measures 151 -- 8.2 Concentration for independent permutations 155 -- 8.3 Subsequences, percolation, assignment 159 -- 8.4 The spin glass free energy 163 -- 8.5 Concentration of random matrices 167 -- Notes and Remarks 170 -- REFERENCES 171 -- INDEX 181.
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Item type Current location Call number Status Date due Barcode Item holds
Book Skoltech library
Shelves 		QA273.43 .L43 2001 (Browse shelf) Available 2000006606
Total holds: 0

Includes bibliographical references (p. 171-179) and index.

Machine generated contents note: INTRODUCTION vii -- 1. CONCENTRATION FUNCTIONS -- AND INEQUALITIES 1 -- 1.1 First examples 1 -- 1.2 Concentration functions 3 -- 1.3 Deviation inequalities 5 -- 1.4 Observable diameter 14 -- 1.5 Expansion coefficient 15 -- 1.6 Laplace bounds and infimum-convolutions 16 -- Notes and Remarks 21 -- 2. ISOPERIMETRIC AND FUNCTIONAL EXAMPLES 23 -- 2.1 Isoperimetric examples 23 -- 2.2 Brunn-Minkowski inequalities 32 -- 2.3 Semigroup tools 38 -- Notes and Remarks 44 -- 3. CONCENTRATION AND GEOMETRY 47 -- 3.1 Spectrum and concentration 47 -- 3.2 Spectral and diameter bounds 53 -- 3.3 L6vy families 55 -- 3.4 Topological applications 57 -- 3.5 Euclidean sections of convex bodies 60 -- Notes and Remarks 65 -- 4. CONCENTRATION IN PRODUCT SPACES 67 -- 4.1 Martingale methods 67 -- 4.2 Convex hull approximation 72 -- 4.3 Control by several points 79 -- 4.4 Convex infimum-convolution 82 -- 4.5 The exponential distribution 83 -- Notes and Remarks 89 -- 5. ENTROPY AND CONCENTRATION 91 -- 5.1 Logarithmic Sobolev inequalities and concentration 91 -- 5.2 Product measures 97 -- 5.3 Modified logarithmic Sobolev inequalities 101 -- 5.4 Discrete settings 108 -- 5.5 Covariance identities 114 -- Notes and Remarks 115 -- 6. TRANSPORTATION COST INEQUALITIES 117 -- 6.1 Information inequalities and concentration 117 -- 6.2 Quadratic transportation cost inequalities 122 -- 6.3 Transportation for product and non-product measures 126 -- Notes and Remarks 132 -- 7. SHARP BOUNDS ON GAUSSIAN -- AND EMPIRICAL PROCESSES 133 -- 7.1 Gaussian processes 133 -- 7.2 Bounds on empirical processes 138 -- 7.3 Sharper bounds via the entropic method 142 -- Notes and Remarks 149 -- 8. SELECTED APPLICATIONS 151 -- 8.1 Concentration of harmonic measures 151 -- 8.2 Concentration for independent permutations 155 -- 8.3 Subsequences, percolation, assignment 159 -- 8.4 The spin glass free energy 163 -- 8.5 Concentration of random matrices 167 -- Notes and Remarks 170 -- REFERENCES 171 -- INDEX 181.

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