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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.
TRITA-MAT-E, 2013:47
National Category
URN: urn:nbn:se:kth:diva-129761OAI: diva2:653724
Subject / course
Educational program
Master of Science in Engineering - Vehicle Engineering
Available from: 2013-10-05 Created: 2013-10-04 Last updated: 2013-10-05Bibliographically approved

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