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Concentration inequalities with exch...

Chatterjee, Sourav.

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Concentration inequalities with exchangeable pairs.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Concentration inequalities with exchangeable pairs./
Author:	Chatterjee, Sourav.
Description:	105 p.
Notes:	Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2140.
Contained By:	Dissertation Abstracts International66-04B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3171763
ISBN:	0542086433

Concentration inequalities with exchangeable pairs.
Chatterjee, Sourav.

Concentration inequalities with exchangeable pairs. - 105 p.

Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2140.

Thesis (Ph.D.)--Stanford University, 2005.

The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random variables, since that is where the power of Stein's method is fully realized. Because the theory is quite abstract, we have tried to put in as many examples as possible. Some of the highlighted applications are as follows: (a) We shall find an easily verifiable condition under which a popular heuristic technique originating from physics, known as the "mean field equations" method, is valid. No such condition is currently known. (b) We shall present a way of using couplings to derive concentration inequalities. Although couplings are routinely used for proving decay of correlations, no method for using couplings to derive concentration bounds is available in the literature. This will be used to obtain (c) concentration inequalities with explicit constants under Dobrushin's condition of weak dependence. (d) We shall give a method for obtaining concentration of Haar measures using convergence rates of related random walks on groups. Using this technique and one of the numerous available results about rates of convergence of random walks, we will then prove (e) a quantitative version of Voiculescu's celebrated connection between random matrix theory and free probability.

ISBN: 0542086433Subjects--Topical Terms:

517247
Statistics.

Concentration inequalities with exchangeable pairs.
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100 1 $a Chatterjee, Sourav. $3 1908780
245 1 0 $a Concentration inequalities with exchangeable pairs.
300 $a 105 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2140.
500 $a Adviser: Persi Diaconis.
502 $a Thesis (Ph.D.)--Stanford University, 2005.
520 $a The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random variables, since that is where the power of Stein's method is fully realized. Because the theory is quite abstract, we have tried to put in as many examples as possible. Some of the highlighted applications are as follows: (a) We shall find an easily verifiable condition under which a popular heuristic technique originating from physics, known as the "mean field equations" method, is valid. No such condition is currently known. (b) We shall present a way of using couplings to derive concentration inequalities. Although couplings are routinely used for proving decay of correlations, no method for using couplings to derive concentration bounds is available in the literature. This will be used to obtain (c) concentration inequalities with explicit constants under Dobrushin's condition of weak dependence. (d) We shall give a method for obtaining concentration of Haar measures using convergence rates of related random walks on groups. Using this technique and one of the numerous available results about rates of convergence of random walks, we will then prove (e) a quantitative version of Voiculescu's celebrated connection between random matrix theory and free probability.
590 $a School code: 0212.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 0 $a Stanford University. $3 754827
773 0 $t Dissertation Abstracts International $g 66-04B.
790 1 0 $a Diaconis, Persi, $e advisor
790 $a 0212
791 $a Ph.D.
792 $a 2005
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3171763