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E-raamat: Convexity and Concentration

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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.
Part I Probability and Concentration
Interpolation of Probability Measures on Graphs
3(30)
Erwan Hillion
Entropy and Thinning of Discrete Random Variables
33(22)
Oliver Johnson
Concentration of Measure Principle and Entropy-Inequalities
55(52)
Paul-Marie Samson
Structured Random Matrices
107(50)
Ramon van Handel
Rates of Convergence for Empirical Spectral Measures: A Soft Approach
157(26)
Elizabeth S. Meckes
Mark W. Meckes
Concentration of Measure Without Independence: A Unified Approach Via the Martingale Method
183(28)
Aryeh Kontorovich
Maxim Raginsky
Strong Data-Processing Inequalities for Channels and Bayesian Networks
211(40)
Yury Polyanskiy
Yihong Wu
An Application of a Functional Inequality to Quasi-Invariance in Infinite Dimensions
251(16)
Maria Gordina
Borell's Formula on a Riemannian Manifold and Applications
267(18)
Joseph Lehec
Fourth Moments and Products: Unified Estimates
285(12)
Ivan Nourdin
Giovanni Peccati
Asymptotic Expansions for Products of Characteristic Functions Under Moment Assumptions of Non-integer Orders
297(64)
Sergey G. Bobkov
Part II Convexity and Concentration for Sets and Functions
Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies
361(30)
Vitali Milman
Liran Rotem
Randomized Isoperimetric Inequalities
391(36)
Grigoris Paouris
Peter Pivovarov
Forward and Reverse Entropy Power Inequalities in Convex Geometry
427(60)
Mokshay Madiman
James Melbourne
Peng Xu
Log-Concave Functions
487(38)
Andrea Colesanti
On Some Problems Concerning Log-Concave Random Vectors
525(16)
Rafal Latala
Stability Results for Some Geometric Inequalities and Their Functional Versions
541(24)
Umut Caglar
Elisabeth M. Werner
Measures of Sections of Convex Bodies
565(12)
Alexander Koldobsky
On Isoperimetric Functions of Probability Measures Having Log-Concave Densities with Respect to the Standard Normal Law
577(8)
Sergey G. Bobkov
Counting Integer Points in Higher-Dimensional Polytopes
585(28)
Alexander Barvinok
The Chain Rule Operator Equation for Polynomials and Entire Functions
613
Hermann Konig
Vitali Milman