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Convexity and Concentration

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 th...

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Corporate Author: SpringerLink (Online service)
Other Authors: Carlen, Eric. (Editor, http://id.loc.gov/vocabulary/relators/edt), Madiman, Mokshay. (Editor, http://id.loc.gov/vocabulary/relators/edt), Werner, Elisabeth M. (Editor, http://id.loc.gov/vocabulary/relators/edt)
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2017.
Edition:1st ed. 2017.
Series:The IMA Volumes in Mathematics and its Applications, 161
Subjects:
Convex geometry .
Discrete geometry.
Probabilities.
Convex and Discrete Geometry.
Probability Theory and Stochastic Processes.
Online Access:https://doi.org/10.1007/978-1-4939-7005-6
Table of 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.

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