Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2020-2022

ISBN-13: 9783031262999 / Angielski

Ronen Eldan; Alexander Litvak; Bo'az Klartag

Opis

This book 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 is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.

Spis treści

Preface by the Editors

Extended Foreword by V. Milman - “Asymptotic Geometric Analysis: Achievements and Perspective”

1. S. Arunschalam, O. Regev And P. Yao - “On The Gaussian Surface Area Of Spectrahedra”

2. S. Bobkov, G. P. Chistyakov And F. Gotze - “Asymptotic Expansions And Two- Sided Bounds In Randomized Central Limit Theorems”

3. K. J. Boroczky And P. Kalantzopoulos - “About The Case Of Equality In The Reverse Brascamp-Lieb Inequality”.

4. P. Cattiaux And A. Guillin - “A Journey With The Integrated #2 Criterion And Its Weak Forms”.

5. S. Chewi - “The Entropic Barrier Is N-Self-Concordant” 

6. B. Klartag And S. Sodin - “Local Tail Bounds For Polynomials On The Discrete Cube”.

7. S. Mendelson And G. Paouris - “Stable Recovery And The Coordinate Small-Ball Behaviour Of Random Vectors”

8. D. Mikulincer And Y. Shenfeld - “On The Lipschitz Properties Of Transportation Along Heat Flows”.

9. P. Nayar And J. Rutkowski - “A Short Direct Proof Of The Ivanisvili-Volberg Inequality”

10. L. Rotem - “The Anisotropic Total Variation And Surface Area Measures”.

11. M. Sellke - “Chasing Convex Bodies Optimally”.

12. M. Lotz And J. A. Tropp - “Sharp Phase Transitions In Euclidean Integral Geometry”.