{"id":{"repo_id":"york","oai_identifier":"oai:yorkspace.library.yorku.ca:10315/41894"},"canonical_url":"https://search.dev.ndltd.org/etd/york/oai:yorkspace.library.yorku.ca:10315/41894","repository":{"repo_id":"york","name":"York University","base_url":"https://yorkspace.library.yorku.ca/oai/request"},"display":{"title":"Second-order finite free probability","abstract":"Finite 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.","abstract_html":"Finite 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.","abstract_has_math":false,"creators":["McConnell, Curran"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Bergeron, Nantel"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-03-16","date_published":"2024-03-16","updated_at":"2026-07-24T06:33:49Z","subjects":["Mathematics","Theoretical mathematics"],"languages":["en"],"rights":["Author owns copyright, except where explicitly noted. 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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."]},{"key":"dc:title","label":"Title","values":["Second-order finite free probability"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bergeron, Nantel"],"dc:creator":["McConnell, Curran"],"dc:date.accessioned":["2024-03-18T18:01:33Z"],"dc:date.available":["2024-03-18T18:01:33Z"],"dc:date.issued":["2024-03-16"],"dc:description.abstract":["Finite 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.uri":["https://hdl.handle.net/10315/41894"],"dc:language":["en"],"dc:rights":["Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests."],"dc:subject":["Mathematics","Theoretical mathematics"],"dc:title":["Second-order finite free probability"],"dc:type":["Electronic Thesis or Dissertation"]},"updated_at":"2026-07-24T06:33:49Z"}