Lecture Notes in Mathematics

Geometric Aspects of Functional Analysis

Israel Seminar (GAFA) 2017-2019 Volume II

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

Vorschau
  • 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
Weitere Vorteile

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Über dieses Buch

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.

Inhaltsverzeichnis (16 Kapitel)

Inhaltsverzeichnis (16 Kapitel)
  • A Generalized Central Limit Conjecture for Convex Bodies

    Seiten 1-41

    Jiang, Haotian (et al.)

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

    Seiten 43-63

    Klartag, Bo’az (et al.)

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

    Seiten 65-94

    Latała, Rafał (et al.)

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

    Seiten 95-123

    Li, Jiange (et al.)

  • Small Ball Probability for the Condition Number of Random Matrices

    Seiten 125-137

    Litvak, Alexander E. (et al.)

Dieses Buch kaufen

eBook 21,39 €
42,79 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
  • ISBN 978-3-030-46762-3
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: EPUB, PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Softcover 26,74 €
53,49 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
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Bibliografische Information

Bibliographic Information
Buchtitel
Geometric Aspects of Functional Analysis
Buchuntertitel
Israel Seminar (GAFA) 2017-2019 Volume II
Herausgeber
  • Bo'az Klartag
  • Emanuel Milman
Titel der Buchreihe
Lecture Notes in Mathematics
Buchreihen Band
2266
Copyright
2020
Verlag
Springer International Publishing
Copyright Inhaber
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
Buchreihen ISSN
0075-8434
Auflage
1
Seitenzahl
X, 348
Anzahl der Bilder
7 schwarz-weiß Abbildungen, 1 Abbildungen in Farbe
Themen