References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Gaussian fluctuations in some determinantal processesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2007 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2007. , vii, 27 p.
##### Series

Trita-MAT, ISSN 1401-2286 ; 07-MA-02
##### Keyword [en]

Random matrices, limit theorems
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-4343ISBN: 978-91-7178-603-6OAI: oai:DiVA.org:kth-4343DiVA: diva2:11902
##### Public defence

2007-05-04, Kollegiesalen, F3, KTH, Lindstedtsvägen 26, 14:00
##### Opponent

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##### Supervisors

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#####

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##### Note

QC 20100716Available from: 2007-04-20 Created: 2007-04-20 Last updated: 2010-07-16Bibliographically approved
##### List of papers

This thesis consists of two parts, Papers A and B, in which some stochastic processes, originating from random matrix theory (RMT), are studied.

In the first paper we study the fluctuations of the kth largest eigenvalue,* x**k*, of the Gaussian unitary ensemble (GUE). That is, let* N *be the dimension of the matrix and k depend on N in such a way that k and* N-k* both tend to infinity as *N* - ∞. The main result is that xk, when appropriately rescaled, converges in distribution to a Gaussian random variable as *N* → ∞. Furthermore, if* k*_{1} < ...<* k**m* are such that* k**1*, *k**i*_{+1} - *k**i*_{ }and *N *- *k**m*_{,} *i * =1, ... ,m - 1, tend to infinity as *N* → ∞ it is shown that (*x**k*_{1} , ... ,* x**km*) is multivariate Gaussian in the rescaled *N* → ∞ limit.

In the second paper we study the Airy process,* ***A**(t), and prove that it fluctuates like a Brownian motion on a local scale. We also prove that the Discrete polynuclear growth process (PNG) fluctuates like a Brownian motion in a scaling limit smaller than the one where one gets the Airy process.

1. Gaussian fluctuations of eigenvalues in the GUE$(function(){PrimeFaces.cw("OverlayPanel","overlay11900",{id:"formSmash:j_idt503:0:j_idt507",widgetVar:"overlay11900",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Local Gaussian fluctuations in the Airy and Discrete PNG processes$(function(){PrimeFaces.cw("OverlayPanel","overlay11901",{id:"formSmash:j_idt503:1:j_idt507",widgetVar:"overlay11901",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});