Carlen E., Madiman M, Werner E.M. (Eds.) Convexity and Concentration

Springer Science+Business Media LLC, 2017. — 620 p. — (The IMA Volumes in Mathematics and its Applications 161) — ISBN: 9781493970049.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.Interpolation of Probability Measures on Graphs
Entropy and Thinning of Discrete Random Variables
Concentration of Measure Principle and Entropy-Inequalities
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
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