Geometric Aspects of Functional Analysis : Israel Seminar (GAFA) 2020-2022 / edited by Ronen Eldan, Bo'az Klartag, Alexander Litvak, Emanuel Milman.

Format:

Book

Author/Creator:

Eldan, Ronen.

Contributor:

Klartag, Bo'az.

Litvak, Alexander.

Milman, Emanuel.

Eldan, Ronen.

Series:

Lecture Notes in Mathematics, 1617-9692 ; 2327

Language:

English

Subjects (All):

Functional analysis.

Convex geometry.

Discrete geometry.

Probabilities.

Functional Analysis.

Convex and Discrete Geometry.

Probability Theory.

Local Subjects:

Functional Analysis.

Convex and Discrete Geometry.

Probability Theory.

Physical Description:

1 online resource (443 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

Summary:

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.

Contents:

Cover

Front Matter

Asymptotic Geometric Analysis: Achievements and Perspective

On the Gaussian Surface Area of Spectrahedra

Asymptotic Expansions and Two-Sided Bounds in Randomized Central Limit Theorems

The Case of Equality in Geometric Instances of Barthe's Reverse Brascamp-Lieb Inequality

A Journey with the Integrated Γ 2 Criterion and its Weak Forms

The Entropic Barrier Is n-Self-Concordant

Local Tail Bounds for Polynomials on the Discrete Cube

Stable Recovery and the Coordinate Small-Ball Behaviour of Random Vectors

On the Lipschitz Properties of Transportation Along Heat Flows

A Short Direct Proof of the Ivanisvili-Volberg Inequality

The Anisotropic Total Variation and Surface Area Measures

Chasing Convex Bodies Optimally

Shephard's Inequalities, Hodge-Riemann Relations, and a Conjecture of Fedotov

The Local Logarithmic Brunn-Minkowski Inequality for Zonoids

Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices

Back Matter.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Eldan, Ronen Geometric Aspects of Functional Analysis

ISBN:

3-031-26300-6

OCLC:

1402029441