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Optimal upper bound for the infinity...

Wang, Ke.

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Optimal upper bound for the infinity norm of eigenvectors of random matrices.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Optimal upper bound for the infinity norm of eigenvectors of random matrices./
Author:	Wang, Ke.
Description:	81 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
Contained By:	Dissertation Abstracts International75-01B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3597929
ISBN:	9781303462931

Optimal upper bound for the infinity norm of eigenvectors of random matrices.
Wang, Ke.

Optimal upper bound for the infinity norm of eigenvectors of random matrices. - 81 p.

Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.

Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 2013.

Let Mn be a random Hermitian (or symmetric) matrix whose upper diagonal and diagonal entries are independent random variables with mean zero and variance one. It is well known that the empirical spectral distribution (ESD) converges in probability to the semicircle law supported on [--2, 2]. In this thesis we study the local convergence of ESD to the semicircle law. One main result is that if the entries of M n are bounded, then the semicircle law holds on intervals of scale log n/n. As a consequence, we obtain the delocalization result for the eigenvectors, i.e., the upper bound for the infinity norm of unit eigenvectors corresponding to eigenvalues in the bulk of spectrum, is O( logn/n ). The bound is the same as the infinity norm of a vector chosen uniformly on the unit sphere in Rn . We also study the local version of Marchenko-Pastur law for random covariance matrices and obtain the optimal upper bound for the infinity norm of singular vectors. This is joint work with V. Vu.

ISBN: 9781303462931Subjects--Topical Terms:

515831
Mathematics.

Optimal upper bound for the infinity norm of eigenvectors of random matrices.
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020 $a 9781303462931
035 $a (MiAaPQ)AAI3597929
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100 1 $a Wang, Ke. $3 1057908
245 1 0 $a Optimal upper bound for the infinity norm of eigenvectors of random matrices.
300 $a 81 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
500 $a Adviser: Van Vu.
502 $a Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 2013.
520 $a Let Mn be a random Hermitian (or symmetric) matrix whose upper diagonal and diagonal entries are independent random variables with mean zero and variance one. It is well known that the empirical spectral distribution (ESD) converges in probability to the semicircle law supported on [--2, 2]. In this thesis we study the local convergence of ESD to the semicircle law. One main result is that if the entries of M n are bounded, then the semicircle law holds on intervals of scale log n/n. As a consequence, we obtain the delocalization result for the eigenvectors, i.e., the upper bound for the infinity norm of unit eigenvectors corresponding to eigenvalues in the bulk of spectrum, is O( logn/n ). The bound is the same as the infinity norm of a vector chosen uniformly on the unit sphere in Rn . We also study the local version of Marchenko-Pastur law for random covariance matrices and obtain the optimal upper bound for the infinity norm of singular vectors. This is joint work with V. Vu.
520 $a In the last chapter, we discuss the delocalization properties for the adjacency matrices of Erdo&huml;s-Renyi random graph. This is part of some earlier results joint with L. Tran and V. Vu.
590 $a School code: 0190.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a Rutgers The State University of New Jersey - New Brunswick. $b Mathematics. $3 2096812
773 0 $t Dissertation Abstracts International $g 75-01B(E).
790 $a 0190
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3597929