The Concentration of Measure Phenomenon (Mathematical Surveys and Monographs)

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9780821837924: The Concentration of Measure Phenomenon (Mathematical Surveys and Monographs)
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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.

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Ledoux, Michel
Editorial: American Mathematical Society (2005)
ISBN 10: 0821837923 ISBN 13: 9780821837924
Nuevos Paperback Cantidad: > 20
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Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: New. Brand new. We distribute directly for the publisher. 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 Lévy. 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. Nº de ref. de la librería 1006240195

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Ledoux, Michel
Editorial: American Mathematical Society (2005)
ISBN 10: 0821837923 ISBN 13: 9780821837924
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Descripción American Mathematical Society, 2005. Estado de conservación: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! 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 presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications and product measures. Nº de ref. de la librería ABE_book_new_0821837923

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Ledoux, Michel
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ISBN 10: 0821837923 ISBN 13: 9780821837924
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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0821837923

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Descripción American Mathematical Society 2005-02-14, 2005. Paperback. Estado de conservación: New. 0821837923. Nº de ref. de la librería 534240

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Descripción Amer Mathematical Society, 2001. Paperback. Estado de conservación: Brand New. 179 pages. 9.75x6.75x0.50 inches. In Stock. Nº de ref. de la librería 0821837923

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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: New. Nº de ref. de la librería P110821837923

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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: New. Nº de ref. de la librería SONG0821837923

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