Concentration and Gaussian Approximation for Randomized Sums: 104 (Probability Theory and Stochastic Modelling, 104) - Tapa dura

Götze, Friedrich; Chistyakov, Gennadiy; Bobkov, Sergey

 
9783031311482: Concentration and Gaussian Approximation for Randomized Sums: 104 (Probability Theory and Stochastic Modelling, 104)
Tapa dura
ISBN 10: 3031311485 ISBN 13: 9783031311482
Editorial: Springer, 2023

Sinopsis

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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De la contraportada

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, thelatter 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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2023
Idioma
Inglés
ISBN 10 
3031311485
ISBN 13 
9783031311482
Encuadernación
Tapa dura
Número de páginas
454
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Otras ediciones populares con el mismo título

9783031311505: Concentration and Gaussian Approximation for Randomized Sums

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ISBN 10:  3031311507 ISBN 13:  9783031311505
Editorial: Springer, 2023
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