Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Probability in Banach Spaces

Isoperimetry and Processes

Authors: Ledoux, Michel, Talagrand, Michel

  • A very comprehensive book which develops a wide variety of the methods existing in this field
  • An event for mathematicians working or interested in probability in Banach spaces
  • a presentation of the main aspects of the theory of probability in Banach spaces
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About this book

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

About the authors

Michel Ledoux held first a research position with CNRS, and since 1991 is Professor at the University of Toulouse. He is moreover, since 2010, a senior member of the Institut Universitaire de France, having been also a junior member from 1997 to 2002. He has held associate editor appointments for various journals, including the Annals of Probability and Probability Theory and Related Fields (current). His research interests centre on probability, random matrices, logarithmic Sobolev inequalities, probability in Banach spaces.

Michel Talagrand has held a research position with the CNRS since 1974. His thesis was directed by Gustave Choquet and his interests revolve around the theory of stochastic processes and probability in Banach spaces, as well as the mathematical theory of spin glasses.  He was invited to deliver a lecture at the International Congress of Mathematicians in 1990, and to deliver a plenary lecture at the same congress in 1998. He received the Loeve Prize (1995) and the Fermat Prize (1997) for his work in probability theory. He was elected to the Paris Academy of Sciences in 2004.

Reviews

This book gives an excellent, almost complete account of the whole subject of probability in Banach spaces, a branch of probability theory that has undergone vigorous development... There is no doubt in the reviewer's mind that this book [has] become a classic.

                                                                           MathSciNet

As the authors state, "this book tries to present some of the main aspects of the theory of probability in Banach spaces, from the foundation of the topic to the latest developments and current research questions''. The authors have succeeded admirably…  This very comprehensive book develops a wide variety of the methods existing … in probability in Banach spaces. … It [has] become an event for mathematicians…                                            

                                                                  Zentralblatt MATH

Table of contents (3 chapter)

  • Introduction

    Michel Ledoux, Michel Talagrand

    Pages 1-6

    Buy Chapter $29.95
  • Notation

    Michel Ledoux, Michel Talagrand

    Pages 7-12

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  • Rademacher Averages

    Michel Ledoux, Michel Talagrand

    Pages 89-121

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Buy this book

eBook $69.99 net
( price for USA )
  • ISBN 978-3-642-20212-4
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $99.00 net
( price for USA )
  • ISBN 978-3-642-08087-6
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days
Softcover $74.95 net
( price for USA )
  • ISBN 978-3-642-20211-7
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Probability in Banach Spaces
Book Subtitle
Isoperimetry and Processes
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
23
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-20212-4
DOI
10.1007/978-3-642-20212-4
Softcover ISBN
978-3-642-08087-6
Softcover ISBN
978-3-642-20211-7
Series ISSN
0071-1136
Edition Number
1
Topics