Concentration and Gaussian Approximation for Randomized Sums (1st ed. 2023)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Probability Theory and Stochastic Modelling, 104
Release date:	May 2023
First published:	2023
Authors:	Sergey Bobkov • Gennadiy Chistyakov • Friedrich Götze
Dimensions:	235 x 155mm (L x W)
Pages:	434
Edition:	1st ed. 2023
ISBN-13:	978-3-03-131148-2
Categories:	Books
LSN:	3-03-131148-5
Barcode:	9783031311482

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