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portada Concentration and Gaussian Approximation for Randomized Sums
Type
Physical Book
Author
Publisher
Language
English
Pages
434
Format
Paperback
ISBN13
9783031311512
Categories

Concentration and Gaussian Approximation for Randomized Sums

Sergey Bobkov (Author) · Gennadiy Chistyakov (Author) · Friedrich Götze (Author) · Springer · Paperback

Concentration and Gaussian Approximation for Randomized Sums - Bobkov, Sergey ; Chistyakov, Gennadiy ; Götze, Friedrich

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Synopsis "Concentration and Gaussian Approximation for Randomized Sums"

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.

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