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

Essays on Random Matrix Theory and A...

Orejola, Oliver,

Linked to FindBook

Google Book

Amazon

博客來

Essays on Random Matrix Theory and Applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Essays on Random Matrix Theory and Applications // Oliver Orejola.
Author:	Orejola, Oliver,
Description:	1 electronic resource (170 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-01, Section: B.
Contained By:	Dissertations Abstracts International86-01B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31294591
ISBN:	9798383202173

Essays on Random Matrix Theory and Applications /
Orejola, Oliver,

Essays on Random Matrix Theory and Applications /Oliver Orejola. - 1 electronic resource (170 pages)

Source: Dissertations Abstracts International, Volume: 86-01, Section: B.

This thesis explores convergence phenomena and statistical methodologies within high-dimensional frameworks. The first aspect investigates the convergence behavior of the empirical spectral distribution of wavelet random matrices stemming from self-similar processes, elucidating its relationship with the distribution of Hurst exponents. By assuming increasing sample sizes, dimensions, and scale, the thesis establishes weak convergence in probability of the empirical distribution of rescaled wavelet log-eigenvalues.The second facet introduces an algorithmic approach for discerning the underlying Hurst modes governing high-dimensional fractal systems. Leveraging spectral clustering on large wavelet random matrices' empirical spectral distributions, the methodology achieves consistent estimation of Hurst modes. Through Monte Carlo simulations, it demonstrates superior efficacy over conventional clustering techniques based on Gaussian mixture modeling, enhancing our ability to identify and characterize fractal structures.In the last portion of this work, we extend classical matrix concentration inequalities as to generalize the Hoeffding and the matrix Bernstein-type inequalities. By relaxing traditional boundedness assumptions and considering sub-Gaussian and sub-exponential tail conditions on matrix norms, it broadens the applicability of concentration inequalities.

English

ISBN: 9798383202173Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Mixed-Gaussian distribution

Essays on Random Matrix Theory and Applications /
LDR:02879nmm a22004453i 4500 001 2430751
005 20250603111610.5
006 m o d
007 cr|nu||||||||
008 261011s2024 miu||||||m |||||||eng d
020 $a 9798383202173
035 $a (MiAaPQD)AAI31294591
035 $a AAI31294591
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Orejola, Oliver, $e author. $3 3819231
245 1 0 $a Essays on Random Matrix Theory and Applications / $c Oliver Orejola.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 1 electronic resource (170 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-01, Section: B.
500 $a Advisors: Didier, Gustavo Committee members: McLaughlin, Kenneth; Pushon-Smith, Samuel; Glatt-Holtz, Nathan; Mazzuca, Guido.
502 $b Ph.D. $c Tulane University $d 2024.
520 $a This thesis explores convergence phenomena and statistical methodologies within high-dimensional frameworks. The first aspect investigates the convergence behavior of the empirical spectral distribution of wavelet random matrices stemming from self-similar processes, elucidating its relationship with the distribution of Hurst exponents. By assuming increasing sample sizes, dimensions, and scale, the thesis establishes weak convergence in probability of the empirical distribution of rescaled wavelet log-eigenvalues.The second facet introduces an algorithmic approach for discerning the underlying Hurst modes governing high-dimensional fractal systems. Leveraging spectral clustering on large wavelet random matrices' empirical spectral distributions, the methodology achieves consistent estimation of Hurst modes. Through Monte Carlo simulations, it demonstrates superior efficacy over conventional clustering techniques based on Gaussian mixture modeling, enhancing our ability to identify and characterize fractal structures.In the last portion of this work, we extend classical matrix concentration inequalities as to generalize the Hoeffding and the matrix Bernstein-type inequalities. By relaxing traditional boundedness assumptions and considering sub-Gaussian and sub-exponential tail conditions on matrix norms, it broadens the applicability of concentration inequalities.
546 $a English
590 $a School code: 0235
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Statistics. $3 517247
653 $a Mixed-Gaussian distribution
653 $a Random matrices
653 $a Spectral clustering
653 $a Wavelets
653 $a Convergence behavior
653 $a Concentration inequalities
690 $a 0405
690 $a 0642
690 $a 0463
710 2 $a Tulane University. $b Mathematics. $e degree granting institution. $3 3819232
720 1 $a Didier, Gustavo $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-01B.
790 $a 0235
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31294591