Higher Order Moments and Free Cumulants of Complex Wigner Matrices

dc.contributor.authorMunoz George, Danielen
dc.contributor.departmentMathematics and Statisticsen
dc.contributor.supervisorMingo, James A
dc.date.accessioned2023-06-12T18:48:34Z
dc.date.available2023-06-12T18:48:34Z
dc.degree.grantorQueen's University at Kingstonen
dc.description.abstractThe main object of this thesis is a random matrix model known as the Wigner model. We investigate the higher order moments and free cumulants of a complex Wigner matrix. It is well known that the first order moments and free cumulants of this model are described by the Catalan numbers and the semicircle law, this constitutes part of the work done by Wigner in the 1950s. Later on, in 2020, Male, Mingo, Péché and Speicher answered this question for the second order case, these are known as the fluctuation moments. In this thesis, we provide a formula for the third order moments in terms of the set of partitioned permutations. Furthermore, we also present a simple expression for the third order free cumulants. In Chapter 6 we talk about the progress that has been made for any higher order case. We prove that the higher order moments and free cumulants exist as long as we ask for suitable conditions.en
dc.description.degreePhDen
dc.identifier.urihttp://hdl.handle.net/1974/31707
dc.language.isoengen
dc.relation.ispartofseriesCanadian thesesen
dc.rightsQueen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada*
dc.rightsProQuest PhD and Master's Theses International Dissemination Agreement*
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dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.*
dc.rightsAttribution-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nd/3.0/us/*
dc.subjectWigneren
dc.subjectRandom matrix theoryen
dc.subjectFree Probabilityen
dc.subjectHigher order momentsen
dc.subjectFree cumulantsen
dc.subjectCumulantsen
dc.titleHigher Order Moments and Free Cumulants of Complex Wigner Matricesen
dc.typethesisen
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