Geometric Aspects of Functional Analysis

1. Front Matter

   Pages i-xii

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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

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.

• 80M35, 26A51, 32-XX, 46-XX, 60-XX
• Asymptotic Geometric Analysis
• Functional Analysis
• Spectral Analysis
• Geometric Probability
• Convex Geometry

   

• 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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