Springer Monographs in Mathematics

Superconcentration and Related Topics

Authors: Chatterjee, Sourav

  • First book devoted to the topic of super concentration, chaos and multiple valleys
  • Presents a wide array of examples on the subject
  • Integrates new concepts and gives a systematic account of the history and development of the features of random objects
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  • ISBN 978-3-319-03886-5
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Softcover $109.00
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  • ISBN 978-3-319-35228-2
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About this book

A certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple valleys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach.

Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012.

The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability.

About the authors

Sourav Chatterjee is a Professor of Statistics and Mathematics at Stanford University. He has previously taught at the University of California at Berkeley and at the Courant Institute of Mathematical Sciences. He has won several international awards for his work in probability theory, including the Rollo Davidson Prize (2010), the Doeblin Prize (2012) and the Loève Prize (2013) and has received the invitation to speak at the International Congress of Mathematicians in 2014.

Table of contents (12 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-03886-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-03885-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-319-35228-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Superconcentration and Related Topics
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-03886-5
DOI
10.1007/978-3-319-03886-5
Hardcover ISBN
978-3-319-03885-8
Softcover ISBN
978-3-319-35228-2
Series ISSN
1439-7382
Edition Number
1
Number of Pages
IX, 156
Topics