Convexity and Concentration

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.