Second-order finite free probability

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dc.contributor.advisorBergeron, Nantel
dc.contributor.authorMcConnell, Curran
dc.date.accessioned2024-03-18T18:01:33Z
dc.date.available2024-03-18T18:01:33Z
dc.date.issued2024-03-16
dc.date.updated2024-03-16T10:45:31Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelMaster's
dc.degree.nameMA - Master of Arts
dc.description.abstractFinite free probability is a new field lying at the intersection of random matrix theory and non-commutative probability. It is called “finite” because unlike traditional free probability, which takes the perspective of operators on infinite-dimensional vector spaces, finite free probability focuses on the study of d × d matrices. Both fields study the behaviour of the eigenvalues of random linear transformations under addition. Finite free probability seeks in particular to characterize random matrices in terms of their (random) characteristic polynomials. I studied the covariance between the coefficients of these polynomials, in order to deepen our knowledge of how random characteristic polynomials fluctuate about their expected values. Focusing on a special case related to random unitary matrices, I applied the representation theory of the unitary group to derive a combinatorial summation expression for the covariance.
dc.identifier.urihttps://hdl.handle.net/10315/41894
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectMathematics
dc.subjectTheoretical mathematics
dc.subject.keywordsFree probability
dc.subject.keywordsFinite free probability
dc.subject.keywordsWeingarten calculus
dc.subject.keywordsStatistics
dc.subject.keywordsSecond-order free probability
dc.subject.keywordsUnitary group
dc.subject.keywordsRepresentation theory
dc.titleSecond-order finite free probability
dc.typeElectronic Thesis or Dissertation

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