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Convexity and Concentration

  • Conference proceedings
  • © 2017

Overview

Editors:
  1. Eric Carlen

    1. Department of Mathematics, Rutgers University, Piscataway, USA

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  2. Mokshay Madiman

    1. Department of Mathematical Sciences, University of Delaware, Newark, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Elisabeth M. Werner

    1. Department of Mathematics, Case Western Reserve University, Cleveland, USA

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  • Written by leading experts in the field, providing state of the art results
  • Chapters derived from workshop talks, annual program seminars, and research interests of mathematicians at the IMA
  • Contains many surveys of active research areas, including open problems

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 161)

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Table of contents (21 papers)

  1. Front Matter

    Pages i-x
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  2. Probability and Concentration

    1. Front Matter

      Pages 1-1
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    2. Interpolation of Probability Measures on Graphs

      • Erwan Hillion
      Pages 3-32

    3. Entropy and Thinning of Discrete Random Variables

      • Oliver Johnson
      Pages 33-53

    4. Concentration of Measure Principle and Entropy-Inequalities

      • Paul-Marie Samson
      Pages 55-105

    5. Structured Random Matrices

      • Ramon van Handel
      Pages 107-156

    6. Rates of Convergence for Empirical Spectral Measures: A Soft Approach

      • Elizabeth S. Meckes, Mark W. Meckes
      Pages 157-181

    7. Concentration of Measure Without Independence: A Unified Approach Via the Martingale Method

      • Aryeh Kontorovich, Maxim Raginsky
      Pages 183-210

    8. Strong Data-Processing Inequalities for Channels and Bayesian Networks

      • Yury Polyanskiy, Yihong Wu
      Pages 211-249

    9. An Application of a Functional Inequality to Quasi-Invariance in Infinite Dimensions

      • Maria Gordina
      Pages 251-266

    10. Borell’s Formula on a Riemannian Manifold and Applications

      • Joseph Lehec
      Pages 267-284

    11. Fourth Moments and Products: Unified Estimates

      • Ivan Nourdin, Giovanni Peccati
      Pages 285-295

    12. Asymptotic Expansions for Products of Characteristic Functions Under Moment Assumptions of Non-integer Orders

      • Sergey G. Bobkov
      Pages 297-357

  3. Convexity and Concentration for Sets and Functions

    1. Front Matter

      Pages 359-359
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    2. Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies

      • Vitali Milman, Liran Rotem
      Pages 361-390

    3. Randomized Isoperimetric Inequalities

      • Grigoris Paouris, Peter Pivovarov
      Pages 391-425

    4. Forward and Reverse Entropy Power Inequalities in Convex Geometry

      • Mokshay Madiman, James Melbourne, Peng Xu
      Pages 427-485

    5. Log-Concave Functions

      • Andrea Colesanti
      Pages 487-524

    6. On Some Problems Concerning Log-Concave Random Vectors

      • RafaÅ‚ LataÅ‚a
      Pages 525-539

    7. Stability Results for Some Geometric Inequalities and Their Functional Versions

      • Umut Caglar, Elisabeth M. Werner
      Pages 541-564
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About this book

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.

Editors and Affiliations

  • Department of Mathematics, Rutgers University, Piscataway, USA

    Eric Carlen

  • Department of Mathematical Sciences, University of Delaware, Newark, USA

    Mokshay Madiman

  • Department of Mathematics, Case Western Reserve University, Cleveland, USA

    Elisabeth M. Werner

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