Convexity and Concentration / edited by Eric Carlen, Mokshay Madiman, Elisabeth M. Werner.

Format:

Book

Contributor:

Carlen, Eric., Editor.

Madiman, Mokshay., Editor.

Werner, Elisabeth M., Editor.

Series:

The IMA Volumes in Mathematics and its Applications, 2198-3224 ; 161

Language:

English

Subjects (All):

Convex geometry.

Discrete geometry.

Probabilities.

Convex and Discrete Geometry.

Probability Theory.

Local Subjects:

Convex and Discrete Geometry.

Probability Theory.

Physical Description:

1 online resource (X, 626 p. 6 illus., 5 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2017.

Summary:

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.

Contents:

Part I: Probability and Concentration

Interpolation of Probability Measures on Graphs

Entropy and Thinning of Discrete Random Variables

Structured Random Matrices

Rates of Convergence for Empirical Spectral Measures: A Soft Approach

Concentration of MEasure without Independence: A Unified Approach via the Martingale Method

Strong Data-Processing Inequalities for Channels and Bayesian Networks

An Application of a Functional Inequality to Quasi Invariance in Infinite Dimensions

Borell's Formula on a Riemannian Manifold and Applications

Fourth Moments and Products: Unified Estimates

Asymptotic Expansions for Products of Characteristic Functions Under Moment Assumptions of non-Integer Orders

Part II: Convexity and Concentration for Sets and Functions

Non-Standard Constructions in Convex Geometry: Geometric Means of Convex Bodies

Randomized Isoperimetric Inequalities

Forward and Reverse Entropy Power Inequalities in Convex Geometry

Log-Concave Functions

On Some Problems Concerning Log-Concave Random Vectors

Stability Results for Some Geometric Inequalities and their Functional Versions

Measures of Sections of Convex Bodies

On Isoperimetric Functions of Probability Measures Having Log-Concave Densities with Respect to the Standard Normal Law

Counting Integer Points in Higher-Dimensional Polytopes

The Chain Rule Operator Equation for Polynomials and Entire Functions.

Notes:

Includes bibliographical references at the end of each chapters.

ISBN:

1-4939-7005-4