Overview
- Self-contained book on extensions of Sudakov's theorem
- Discusses weighted sums of random variables and the concentration of their distributions around Gaussian laws
- Contains a detailed exposition of the concentration of measure phenomenon on the unit sphere
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 104)
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Table of contents (21 chapters)
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Front Matter
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Selected Topics on Concentration
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Front Matter
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Analysis on the Sphere
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Front Matter
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First Applications to Randomized Sums
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Front Matter
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Refined Bounds and Rates
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Front Matter
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Keywords
About this book
This book describes extensions of Sudakov's classical result on the concentration of measure phenomenon for weighted sums of dependent random variables. The central topics of the book are weighted sums of random variables and the concentration of their distributions around Gaussian laws. The analysis takes place within the broader context of concentration of measure for functions on high-dimensional spheres. Starting from the usual concentration of Lipschitz functions around their limiting mean, the authors proceed to derive concentration around limiting affine or polynomial functions, aiming towards a theory of higher order concentration based on functional inequalities of log-Sobolev and Poincaré type. These results make it possible to derive concentration of higher order for weighted sums of classes of dependent variables.
While the first part of the book discusses the basic notions and results from probability and analysis which are needed for the remainder of the book, the latter parts provide a thorough exposition of concentration, analysis on the sphere, higher order normal approximation and classes of weighted sums of dependent random variables with and without symmetries.
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Concentration and Gaussian Approximation for Randomized Sums
Authors: Sergey Bobkov, Gennadiy Chistyakov, Friedrich Götze
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-031-31149-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-31148-2Published: 18 May 2023
Softcover ISBN: 978-3-031-31151-2Published: 18 May 2024
eBook ISBN: 978-3-031-31149-9Published: 17 May 2023
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XVII, 434
Topics: Probability Theory and Stochastic Processes, Applications of Mathematics, Statistical Theory and Methods