Convexity and Concentration

Part I. Probability and Concentration

1. Interpolation of Probability Measures on Graphs
Erwan Hillion

2. Entropy and Thinning of Discrete Random Variables
Oliver Johnson

3. Concentration of Measure Principle and Entropy-Inequalities
Paul-Marie Samson

4. Structured Random Matrices
Ramon Handel

5. Rates of Convergence for Empirical Spectral Measures: A Soft Approach
Elizabeth S. Meckes, Mark W. Meckes

6. Concentration of Measure Without Independence: A Unified Approach Via the Martingale Method
Aryeh Kontorovich, Maxim Raginsky

7. Strong Data-Processing Inequalities for Channels and Bayesian Networks
Yury Polyanskiy, Yihong Wu

8. An Application of a Functional Inequality to Quasi-Invariance in Infinite Dimensions
Maria Gordina

9. Borell’s Formula on a Riemannian Manifold and Applications
Joseph Lehec

10. Fourth Moments and Products: Unified Estimates
Ivan Nourdin, Giovanni Peccati

11. Asymptotic Expansions for Products of Characteristic Functions Under Moment Assumptions of Non-integer Orders
Sergey G. Bobkov

Part II. Convexity and Concentration for Sets and Functions

12. Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies
Vitali Milman, Liran Rotem

13. Randomized Isoperimetric Inequalities
Grigoris Paouris, Peter Pivovarov

14. Forward and Reverse Entropy Power Inequalities in Convex Geometry
Mokshay Madiman, James Melbourne, Peng Xu

15. Log-Concave Functions
Andrea Colesanti

16. On Some Problems Concerning Log-Concave Random Vectors
Rafał Latała

17. Stability Results for Some Geometric Inequalities and Their Functional Versions
Umut Caglar, Elisabeth M. Werner

18. Measures of Sections of Convex Bodies
Alexander Koldobsky

19. On Isoperimetric Functions of Probability Measures Having Log-Concave Densities with Respect to the Standard Normal Law
Sergey G. Bobkov

20. Counting Integer Points in Higher-Dimensional Polytopes
Alexander Barvinok

21. The Chain Rule Operator Equation for Polynomials and Entire Functions
Hermann König, Vitali Milman

Keywords: Mathematics, Convex and Discrete Geometry, Probability Theory and Stochastic Processes