Concentration and Gaussian approximation for randomized sums / Sergey Bobkov, Gennadiy Chistyakov, Friedrich Gt̲ze.

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Concentration and Gaussian approximation for randomized sums / Sergey Bobkov, Gennadiy Chistyakov, Friedrich Gt̲ze.

9783031311499 (electronic bk.)
3031311493 (electronic bk.)
9783031311482

Cham : Springer, [2023]

©2023

English

1 online resource (xvii, 434 pages).

10.1007/978-3-031-31149-9 doi

QA273.6

519.2/4

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 Poincar ̌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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed May 24, 2023).

Probability theory and stochastic modelling ; v. 104.

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