MARC Record from Library of Congress

LEADER: 02987cam a22002894a 4500
001 2001041310
003 DLC
005 20050308181544.0
008 010612s2001 riu b 001 0 eng
010 $a 2001041310
020 $a0821828649 (acid-free paper)
040 $aDLC$cDLC$dDLC
042 $apcc
050 00 $aQA273.43$b.L43 2001
082 00 $a519.2$221
100 1 $aLedoux, Michel,$d1958-
245 14 $aThe concentration of measure phenomenon /$cMichel Ledoux.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$cc2001.
300 $ax, 181 p. ;$c27 cm.
490 1 $aMathematical surveys and monographs,$x0076-5376 ;$vv. 89
504 $aIncludes bibliographical references (p. 171-179) and index.
505 8 $aMachine 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.
650 0 $aConcentration functions.
650 0 $aMeasure theory.
650 0 $aProbabilities.
830 0 $aMathematical surveys and monographs ;$vno. 89.
856 41 $3Table of contents$uhttp://www.loc.gov/catdir/toc/fy022/2001041310.html