Concentration and Gaussian Approximation for Randomized Sums is popular PDF and ePub book, written by Sergey Bobkov in 2023-06-18, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Concentration and Gaussian Approximation for Randomized Sums can be Read Online from any device for your convenience.
Concentration and Gaussian Approximation for Randomized Sums Book PDF Summary
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.
Detail Book of Concentration and Gaussian Approximation for Randomized Sums PDF
- Author : Sergey Bobkov
- Release : 18 June 2023
- Publisher : Springer Nature
- ISBN : 9783031311499
- Genre : Mathematics
- Total Page : 438 pages
- Language : English
- PDF File Size : 12,9 Mb
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