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High Dimensional Probability VI

The Banff Volume

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Christian Houdré

    1. Georgia Institute of Technology, Atlanta, USA

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  2. David M. Mason

    1. University of Delaware, Newark, USA

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  3. Jan Rosiński

    1. University of Tennessee, Knoxville, USA

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  4. Jon A. Wellner

    1. University of Washington, Seattle, USA

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  • Gives a unique view on the mathematical methods used by experts to establish limit theorems in probability and statistics, which reside in high dimensions
  • Displays the wide scope of the types of problems to which these methods can be successfully applied
  • Provides a valuable introduction to what is meant by high dimensional probability and exposes fruitful new areas of research in the area

Part of the book series: Progress in Probability (PRPR, volume 66)

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Table of contents (21 papers)

  1. Front Matter

    Pages i-xiii
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  2. Inequalities and Convexity

    1. Front Matter

      Pages 1-1
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    2. Bracketing Entropy of High Dimensional Distributions

      • Fuchang Gao
      Pages 3-17

    3. Slepian’s Inequality, Modularity and Integral Orderings

      • J. Hoffmann-Jørgensen
      Pages 19-53

    4. A More General Maximal Bernstein-type Inequality

      • Péter Kevei, David M. Mason
      Pages 55-62

    5. Maximal Inequalities for Centered Norms of Sums of Independent Random Vectors

      • Rafał Latała
      Pages 63-71

    6. A Probabilistic Inequality Related to Negative Definite Functions

      • Mikhail Lifshits, René L. Schilling, Ilya Tyurin
      Pages 73-80

    7. Optimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities

      • Iosif Pinelis
      Pages 81-93

    8. Strong Log-concavity is Preserved by Convolution

      • Jon A. Wellner
      Pages 95-102

    9. On Some Gaussian Concentration Inequality for Non-Lipschitz Functions

      • Paweł Wolff
      Pages 103-110

  3. Limit Theorems

    1. Front Matter

      Pages 111-111
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    2. Rates of Convergence in the Strong Invariance Principle for Non-adapted Sequences Application to Ergodic Automorphisms of the Torus

      • Jérôme Dedecker, Florence Merlevède, Françoise Pène
      Pages 113-138

    3. On the Rate of Convergence to the Semi-circular Law

      • Friedrich Götze, Alexandre Tikhomirov
      Pages 139-165

    4. Empirical Quantile CLTs for Time-dependent Data

      • James Kuelbs, Joel Zinn
      Pages 167-194

    5. Asymptotic Properties for Linear Processes of Functionals of Reversible or Normal Markov Chains

      • Magda Peligrad
      Pages 195-210

  4. Stochastic Processes

    1. Front Matter

      Pages 211-211
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    2. First Exit of Brownian Motion from a One-sided Moving Boundary

      • Frank Aurzada, Tanja Kramm
      Pages 213-217

    3. On Lévy’s Equivalence Theorem in Skorohod Space

      • Andreas Basse-O’Connor, Jan Rosiński
      Pages 219-225

    4. Continuity Conditions for a Class of Second-order Permanental Chaoses

      • Michael B. Marcus, Jay Rosen
      Pages 227-243

  5. Random Matrices and Applications

    1. Front Matter

      Pages 245-245
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Keywords

About this book

This is a collection of papers by participants at High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada. 

High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other areas of mathematics, statistics, and computer science. These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory.

The papers in this volume show that HDP theory continues to develop new tools, methods, techniques and perspectives to analyze the random phenomena. Both researchers and advanced students will find this book of great use for learning about new avenues of research.​

Editors and Affiliations

  • Georgia Institute of Technology, Atlanta, USA

    Christian Houdré

  • University of Delaware, Newark, USA

    David M. Mason

  • University of Tennessee, Knoxville, USA

    Jan Rosiński

  • University of Washington, Seattle, USA

    Jon A. Wellner

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