Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Gaussian fluctuations of singleeigenvalues intime-dependent GUE
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Gaussiska fluktuationer av egenvärden i tidsberoende GUE (Swedish)
Abstract [en]

This thesis investigates the fluctuations of the eigenvalues of the Gaussian Unitary Ensemble on the basis of numerical simulations performed in the programming environment MATLAB. As is well known: if a Wiener process is defined on the space of Hermitian matrices then the eigenvalues describe a stochastic process known as Dyson Brownian motion. Thus, given a realisation of Dyson Brownian motion, the aim of this thesis is to investigate the distribution of a certain random vector pertaining to fluctuations of the evolution of the eigenvalues using statistical hypothesis tests such as the Kolmogorov-Smirnov test and Mardia’s test for multivariate normality. The results seem to indicate a Gaussian distribution but due to the nature of statistical hypothesis testing the results should be interpreted with caution and as indicative of the underlying distribution.

Abstract [sv]

Denna uppsats undersöker fluktuationerna av egenvärden i matrisensemblen Gaussian Unitary Ensemble på basis av simulationer utförda i programmeringsspråket MATLAB. Det är ett välkänt faktum att om en Wienerprocess definieras på rummet av Hermitiska matriser kommer egenvärdena beskriva en stokastisk process kallad Dyson’s brownska rörelse. Givet en realisering av Dysons brownska rörelse, ¨ar syftet med denna uppsats att undersöka fördelningen av en stokastisk vektor innehållande fluktuationerna av egenvärdena i Dysons Brownska rörelse med hjälp av statistiska hypotesmetoder såsom Kolmogorov- Smirnovs metod och Mardias metod för flerdimensionell normalfördelning. Erhållna resultat tyder p˚a normalfördelning men givet metodiken hos hypotesprövning bör resultaten tolkas som indikativa för den underliggande fördelningen.

Place, publisher, year, edition, pages
2013. , 68 p.
Series
TRITA-MAT-E, 2013:47
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-129761OAI: oai:DiVA.org:kth-129761DiVA: diva2:653724
Subject / course
Mathematics
Educational program
Master of Science in Engineering - Vehicle Engineering
Supervisors
Examiners
Available from: 2013-10-05 Created: 2013-10-04 Last updated: 2013-10-05Bibliographically approved

Open Access in DiVA

fulltext(461 kB)263 downloads
File information
File name FULLTEXT01.pdfFile size 461 kBChecksum SHA-512
1fa52ed2ff77236a1c78a27d7c7884647a8f7231032067f4425569ae28feb937950f3e80114594b7c7e6a04253f24963af673f32faf97cabfa640337c75017c9
Type fulltextMimetype application/pdf

By organisation
Mathematics (Div.)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 263 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 274 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf