Last edited by Mezragore
Sunday, August 2, 2020 | History

8 edition of The Concentration of Measure Phenomenon found in the catalog.

The Concentration of Measure Phenomenon

by Michel Ledoux

  • 13 Want to read
  • 33 Currently reading

Published by American Mathematical Society .
Written in English

    Subjects:
  • Euclidean geometry,
  • Functional analysis,
  • Probability & statistics,
  • Stochastics,
  • Probability & Statistics - General,
  • Mathematics,
  • Concentration functions,
  • Measure theory,
  • Probabilities,
  • Science/Mathematics

  • The Physical Object
    FormatHardcover
    Number of Pages192
    ID Numbers
    Open LibraryOL11420002M
    ISBN 100821828649
    ISBN 109780821828649

    ii Biographical Sketch Meg Walters grew up in Gainesville, FL. She moved to Rochester in to study bassoon performance at the Eastman School of Music and enrolled at the Unive. of new concentration properties. Since then, the concentration-of-measure phenomenon spread out to an im-pressively wide range of illustrations and applications, and became a central tool and viewpoint in the quantitative analysis of a number of asymptotic properties in numerous topics of interest including geometric analysis, probability theory,File Size: 2MB.

    Search the world's most comprehensive index of full-text books. My library. The so-called concentration of measure phenomenon is a powerful tool with applications in different fields of mathematics. Many asymptotic results in probability theory, information theory and dynamical systems such as the law of large numbers, the asymptotic equipartition property, the central limit theorem and Birkhoff's theorem are.

    Ordinarily the concentration of glucose in the blood is maintained at a relatively stable concentration from 80 to mg/dl. The strong reducing properties of glucose made it relatively easy to measure and thus the clinical estimation of circulating glucose was one of the earliest tests available to the clinician. Lecture notes by Lugosi (Essentially superceeded by Concentration Inequalities: A Nonasymptotic Theory of Independence by Boucheron, Lugosi and Massart, but freely available online) Concentration of Measure for the Analysis of Randomized Algorithms by Dubhashi,Panconesi. Terry Tao's blog. Lecture notes on machine learning (e.g. this set by.


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The Concentration of Measure Phenomenon by Michel Ledoux Download PDF EPUB FB2

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 by:   The Concentration of Measure Phenomenon.

It was undoubtedly a necessary task to collect all the results on the concentration of measure during the past years in a monograph. The author did this very successfully and the book is an important contribution to the topic.

It will surely influence further research in this area considerably. 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. 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 Sn S n becomes concentrated around the equator as the dimension gets large.

This property may be interpreted in terms of functions on. Our analysis of kernel matrices for high dimensional data hinges on the concentration of measure phenomenon. Concentration of measure is a property of metric measure spaces that roughly says that regular functions are nearly constant [18, 16, 10].

It can be observed in many spaces. The concentration of measure phenomenon is a notion that was put forward in the ’s by V.

Milman while investigating the asymptotic (i.e., high dimensional) geometry of Banach spaces. It is a notion that has since then proved tremendously. The concentration of measure phenomenon was put forth in the early s by Vitali Milman in his works on the local theory of Banach space, extending an idea going back to the work of Paul Levy.

The idea of concen. One way to phrase the " concentration-of-measure " phenomenon is that, for a Euclidean sphere $S^d$ in $d$ dimensions, for large $d$, "most of the mass is. concentration inequality.

The aim of this course is to investigate the basic mathematical principles behind the concentration of measure phenomenon (e.g., Talagrand’s celebrated inequality), and show its relevance to several difierent areas of mathematics through the following examples: † classical deviation inequalities of probability theory.

With minimal requirement on measure-theoretic knowledge, this book really stands out to bridge computer science/engineering researchers with powerful probabilistic tools. Ideal for self-study of concentration by: 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.

17 Measure Concentration for the Sphere In today’s lecture, we will prove the measure concentration theorem for the sphere.

Recall that this was one of the vital steps in the analysis of the Arora-Rao-Vazirani approximation algorithm for sparsest cut. Most of the material in today’s lecture is adapted from Matousek’sFile Size: KB. The Concentration of Measure Phenomenon 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. He proved that in the gaussian case this property is a consequence of the Prekopa-Leindler inequality.

This method can be easily extended to give a concentration of measure phenomenon for a particular measure associated with uniformly convex spaces whose modulus of convexity satisfies a certain by: 8.

The Concentration of Measure Phenomenon的话题 (全部 条) 什么是话题 无论是一部作品、一个人,还是一件事,都往往可以衍生出许多不同的话题。Author: Michel Ledoux. 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 : Michel Ledoux. 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.

Isoperimetric Inequalities and the Concentration of Measure Phenomenon. Authors; Authors and affiliations inequalities which will be mentioned in their framework throughout the book.

In these final forms however, the isoperimetric inequalities and associated concentration of measure phenomena provide the appropriate ideas for an in depth Author: Michel Ledoux, Michel Talagrand, Michel Talagrand.

The concentration of measure phenomenon was put forth in the early s by Vitali Milman in his works on the local theory of Banach spaces, extending an idea going back to the work of Paul Lévy.

It was further developed in the works of Milman and Gromov, Maurey, Pisier, Schechtman, Talagrand, Ledoux, and others. The Concentration of Measure Phenomenon Michel Ledoux American Mathematical Society. CONTENTS INTRODUCTION vii 1.

CONCENTRATION FUNCTIONS AND INEQUALITIES 1 First examples 1 Concentration for independent permutations Subsequences, percolation, assignment.

Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry.This is the concentration of measure phenomenon, that was promoted most vigorously by V.

Milman. It plays an important role in local theory of Banach spaces, and has become the central concept of the area of probability known as Probability in Banach spaces. (See the book [L-T2], and subsequent work such as [T6], [T7]).Author: Michel Talagrand.Measure Concentration on the Sphere The counterintuitive phenomenon is that your task would be much simpler if the earth were of higher dimension.

For sufficiently large dimension, one round with your10o-mower (or anyα-mower, for fixedα) covers90%(or any desired percentage) of the surface.

This means, the surfacearea of B d is con.