Overview

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 addressedis 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.

Full Product Details

Author:   Bo'az Klartag ,  Emanuel Milman
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2020
Volume:   2256
Weight:   0.545kg
ISBN:  

9783030360191

ISBN 10:   3030360199
Pages:   342
Publication Date:   21 June 2020
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

- Jean Bourgain: In Memoriam. - Gromov’sWaist of Non-radial Gaussian Measures and Radial Non-Gaussian Measures. - Zhang’s Inequality for Log-Concave Functions. - Bobkov’s Inequality via Optimal Control Theory. - Arithmetic Progressions in the Trace of Brownian Motion in Space. - Edgeworth Corrections in Randomized Central Limit Theorems. - Three Applications of the Siegel Mass Formula. - Decouplings for Real Analytic Surfaces of Revolution. - On Discrete Hardy–Littlewood Maximal Functions over the Balls in Zd : Dimension-Free Estimates. - On the Poincaré Constant of Log-Concave Measures. - On Poincaré and Logarithmic Sobolev Inequalities for a Class of Singular Gibbs Measures. - Several Results Regarding the (B)-Conjecture. - A Dimension-Free Reverse Logarithmic Sobolev Inequality for Low-Complexity Functions in Gaussian Space. - Information and Dimensionality of Anisotropic Random GeometricGraphs. - On the Ekeland-Hofer-Zehnder Capacity of Difference Body.

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