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Geometric Aspects of Functional Analysis

Israel Seminar (GAFA) 2014–2016

  • Book
  • © 2017

Overview

Editors:
  1. Bo'az Klartag

    1. School of Mathematical Sciences, Tel Aviv University, Tel-Aviv, Israel

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    You can also search for this editor in PubMed   Google Scholar

  2. Emanuel Milman

    1. Mathematics Department, Technion - Israel Institute of Technology, Haifa, Israel

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2169)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. On Repeated Sequential Closures of Constructible Functions in Valuations

    • Semyon Alesker
    Pages 1-14

  3. Orbit Point of View on Some Results of Asymptotic Theory; Orbit Type and Cotype

    • Limor Ben-Efraim, Vitali Milman, Alexander Segal
    Pages 15-23

  4. Concentration Properties of Restricted Measures with Applications to Non-Lipschitz Functions

    • Sergey G. Bobkov, Piotr Nayar, Prasad Tetali
    Pages 25-53

  5. On Random Walks in Large Compact Lie Groups

    • Jean Bourgain
    Pages 55-63

  6. On a Problem of Farrell and Vershynin in Random Matrix Theory

    • Jean Bourgain
    Pages 65-69

  7. Valuations on the Space of Quasi-Concave Functions

    • Andrea Colesanti, Nico Lombardi
    Pages 71-105

  8. An Inequality for Moments of Log-Concave Functions on Gaussian Random Vectors

    • Nikos Dafnis, Grigoris Paouris
    Pages 107-122

  9. \(\boldsymbol{(s,p)}\)-Valent Functions

    • Omer Friedland, Yosef Yomdin
    Pages 123-136

  10. A Remark on Projections of the Rotated Cube to Complex Lines

    • Efim D. Gluskin, Yaron Ostrover
    Pages 137-149

  11. On the Expectation of Operator Norms of Random Matrices

    • Olivier Guédon, Aicke Hinrichs, Alexander E. Litvak, Joscha Prochno
    Pages 151-162

  12. The Restricted Isometry Property of Subsampled Fourier Matrices

    • Ishay Haviv, Oded Regev
    Pages 163-179

  13. Upper Bound for the Dvoretzky Dimension in Milman-Schechtman Theorem

    • Han Huang, Feng Wei
    Pages 181-186

  14. Super-Gaussian Directions of Random Vectors

    • Bo’az Klartag
    Pages 187-211

  15. A Remark on Measures of Sections of \(\boldsymbol{L}_{p}\)-balls

    • Alexander Koldobsky, Alain Pajor
    Pages 213-220

  16. Sharp Poincaré-Type Inequality for the Gaussian Measure on the Boundary of Convex Sets

    • Alexander V. Kolesnikov, Emanuel Milman
    Pages 221-234

  17. Rigidity of the Chain Rule and Nearly Submultiplicative Functions

    • Hermann König, Vitali Milman
    Pages 235-264

  18. Royen’s Proof of the Gaussian Correlation Inequality

    • Rafał Latała, Dariusz Matlak
    Pages 265-275

  19. A Simple Tool for Bounding the Deviation of Random Matrices on Geometric Sets

    • Christopher Liaw, Abbas Mehrabian, Yaniv Plan, Roman Vershynin
    Pages 277-299

  20. On Multiplier Processes Under Weak Moment Assumptions

    • Shahar Mendelson
    Pages 301-318
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Keywords

About this book

As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical theme in the Local Theory of Banach Spaces which is well represented in this volume is the identification of lower-dimensional structures in high-dimensional objects. More recent applications of high-dimensionality are manifested by contributions in Random Matrix Theory, Concentration of Measure and Empirical Processes. Naturally, the Gaussian measure plays a central role in many of these topics, and is also studied in this volume; in particular, the recent breakthrough proof of the Gaussian Correlation Conjecture is revisited. The interplay of the theory with Harmonic and Spectral Analysis is also well apparent in several contributions. The classical relation to both the primal and dual Brunn-Minkowski theories is also well represented, and related algebraic structures pertaining to valuations and valent functions are discussed. All contributions are original research papers and were subject to the usual refereeing standards.

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Editors and Affiliations

  • School of Mathematical Sciences, Tel Aviv University, Tel-Aviv, Israel

    Bo'az Klartag

  • Mathematics Department, Technion - Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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