東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

High Dimensional Normality of Noisy ...

Marcinek, Jake.

Linked to FindBook

Google Book

Amazon

博客來

High Dimensional Normality of Noisy Eigenvectors.

Record Type:	Electronic resources : Monograph/item
Title/Author:	High Dimensional Normality of Noisy Eigenvectors./
Author:	Marcinek, Jake.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	145 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-11, Section: B.
Contained By:	Dissertations Abstracts International82-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28452502
ISBN:	9798597059617

High Dimensional Normality of Noisy Eigenvectors.
Marcinek, Jake.

High Dimensional Normality of Noisy Eigenvectors. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 145 p.

Source: Dissertations Abstracts International, Volume: 82-11, Section: B.

Thesis (Ph.D.)--Harvard University, 2020.

This item must not be sold to any third party vendors.

We study joint eigenvector distributions for large symmetric matrices in the presence of weak noise. Our main result asserts that every submatrix in the orthogonal matrix of eigenvectors converges to a multidimensional Gaussian distribution. The proof involves analyzing the stochastic eigenstate equation (SEE) which describes the Lie group valued flow of eigenvectors induced by matrix valued Brownian motion. We consider the associated colored eigenvector moment flow defining an SDE on a particle configuration space. This flow extends the eigenvector moment flow to the multicolor setting. However, it is no longer driven by an underlying Markov process on configuration space due to the lack of positivity in the semigroup kernel. Nevertheless, we prove the dynamics admit sufficient averaged decay and contractive properties. This allows us to establish optimal time of relaxation to equilibrium for the colored eigenvector moment flow and prove joint asymptotic normality for eigenvectors. Applications in random matrix theory include the explicit computations of joint eigenvector distributions for general Wigner type matrices and sparse graph models when corresponding eigenvalues lie in the bulk of the spectrum, as well as joint eigenvector distributions for L\\'evy matrices when the eigenvectors correspond to small energy levels.

ISBN: 9798597059617Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Random matrix theory

High Dimensional Normality of Noisy Eigenvectors.
LDR:02436nmm a2200349 4500 001 2280470
005 20210827095958.5
008 220723s2020 ||||||||||||||||| ||eng d
020 $a 9798597059617
035 $a (MiAaPQ)AAI28452502
035 $a (MiAaPQ)vireoharvard3680Marcinek
035 $a AAI28452502
040 $a MiAaPQ $c MiAaPQ
100 1 $a Marcinek, Jake. $3 3558999
245 1 0 $a High Dimensional Normality of Noisy Eigenvectors.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 145 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-11, Section: B.
500 $a Advisor: Yau, Horng-Tzer.
502 $a Thesis (Ph.D.)--Harvard University, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a We study joint eigenvector distributions for large symmetric matrices in the presence of weak noise. Our main result asserts that every submatrix in the orthogonal matrix of eigenvectors converges to a multidimensional Gaussian distribution. The proof involves analyzing the stochastic eigenstate equation (SEE) which describes the Lie group valued flow of eigenvectors induced by matrix valued Brownian motion. We consider the associated colored eigenvector moment flow defining an SDE on a particle configuration space. This flow extends the eigenvector moment flow to the multicolor setting. However, it is no longer driven by an underlying Markov process on configuration space due to the lack of positivity in the semigroup kernel. Nevertheless, we prove the dynamics admit sufficient averaged decay and contractive properties. This allows us to establish optimal time of relaxation to equilibrium for the colored eigenvector moment flow and prove joint asymptotic normality for eigenvectors. Applications in random matrix theory include the explicit computations of joint eigenvector distributions for general Wigner type matrices and sparse graph models when corresponding eigenvalues lie in the bulk of the spectrum, as well as joint eigenvector distributions for L\\'evy matrices when the eigenvectors correspond to small energy levels.
590 $a School code: 0084.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Random matrix theory
653 $a Universality
653 $a Eigenvectors
690 $a 0405
690 $a 0642
710 2 $a Harvard University. $b Mathematics. $3 2049814
773 0 $t Dissertations Abstracts International $g 82-11B.
790 $a 0084
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28452502