Lecture Notes in Mathematics

Geometric Aspects of Functional Analysis

Israel Seminar (GAFA) 2017-2019 Volume II

Editors: Klartag, Bo'az, Milman, Emanuel (Eds.)

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  • Features a unique mixture of papers on convex geometry and high-dimensional analysis
  • Describes state-of-the-art progress in asymptotic geometric analysis
  • Written from an interdisciplinary perspective, relations to differential geometry, information theory and computer science are included
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  • ISBN 978-3-030-46762-3
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valid through 30 de junio de 2021
  • ISBN 978-3-030-46761-6
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About this book

Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.

Table of contents (16 chapters)

Table of contents (16 chapters)
  • A Generalized Central Limit Conjecture for Convex Bodies

    Pages 1-41

    Jiang, Haotian (et al.)

  • The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding

    Pages 43-63

    Klartag, Bo’az (et al.)

  • Two-Sided Estimates for Order Statistics of Log-Concave Random Vectors

    Pages 65-94

    Latała, Rafał (et al.)

  • Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-Concave Densities

    Pages 95-123

    Li, Jiange (et al.)

  • Small Ball Probability for the Condition Number of Random Matrices

    Pages 125-137

    Litvak, Alexander E. (et al.)

Buy this book

eBook $19.99
$44.99 (listprice)
price for Mexico
valid through 30 de junio de 2021
  • ISBN 978-3-030-46762-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $29.99
$59.99 (listprice)
price for Mexico
valid through 30 de junio de 2021
  • ISBN 978-3-030-46761-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Aspects of Functional Analysis
Book Subtitle
Israel Seminar (GAFA) 2017-2019 Volume II
Editors
  • Bo'az Klartag
  • Emanuel Milman
Series Title
Lecture Notes in Mathematics
Series Volume
2266
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-46762-3
DOI
10.1007/978-3-030-46762-3
Softcover ISBN
978-3-030-46761-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 348
Number of Illustrations
7 b/w illustrations, 1 illustrations in colour
Topics