語系:
繁體中文
English
說明(常見問題)
回圖書館首頁
手機版館藏查詢
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Optimal upper bound for the infinity...
~
Wang, Ke.
FindBook
Google Book
Amazon
博客來
Optimal upper bound for the infinity norm of eigenvectors of random matrices.
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Optimal upper bound for the infinity norm of eigenvectors of random matrices./
作者:
Wang, Ke.
面頁冊數:
81 p.
附註:
Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
Contained By:
Dissertation Abstracts International75-01B(E).
標題:
Mathematics. -
電子資源:
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.
LDR
:02104nam a2200289 4500
001
1961008
005
20140701144901.5
008
150210s2013 ||||||||||||||||| ||eng d
020
$a
9781303462931
035
$a
(MiAaPQ)AAI3597929
035
$a
AAI3597929
040
$a
MiAaPQ
$c
MiAaPQ
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
筆 0 讀者評論
館藏地:
全部
電子資源
出版年:
卷號:
館藏
1 筆 • 頁數 1 •
1
條碼號
典藏地名稱
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
W9255836
電子資源
11.線上閱覽_V
電子書
EB
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
評論
新增評論
分享你的心得
Export
取書館
處理中
...
變更密碼
登入