MARC details
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02721nam a22003377a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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IIITD |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20260227135652.0 |
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260227b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780821837924 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
IIITD |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.2 |
| Item number |
LED-C |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Ledoux, Michel |
| 245 ## - TITLE STATEMENT |
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| Title |
The concentration of measure phenomenon |
| Statement of responsibility, etc |
by Michel Ledoux |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Providence : |
| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
©2001 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
x, 181 p. ; |
| Dimensions |
26 cm. |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Mathematical surveys and monographs ; |
| Volume number/sequential designation |
v. 89 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
1. Concentration functions and inequalities |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
2. Isoperimetric and functional examples |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
3. Concentration and geometry |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
4. Concentration in product spaces |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
5. Entropy and concentration |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
6. Transportation cost inequalities |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
7. Sharp bounds on Gaussian and empirical processes |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
8. Selected applications |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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. The 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. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Concentration functions |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Measure theory |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Probabilities |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
Books |
| Source of classification or shelving scheme |
Dewey Decimal Classification |
