Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices

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dc.creatorForrester, Peter J.
dc.creatorRains, Eric M.
dc.date2005-05-25
dc.date.accessioned2026-07-07T05:20:16Z
dc.date.available2026-07-07T05:20:16Z
dc.descriptionIn a recent work Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding eigenvalue p.d.f.'s are beta-generalizations of the classical groups. Left open was the direct calculation of certain Jacobians. We provide the sought direct calculation. Furthermore, we show how a multiplicative rank 1 perturbation of the unitary Hessenberg matrices provides a joint eigenvalue p.d.f generalizing the circular beta-ensemble, and we show how this joint density is related to known inter-relations between circular ensembles. Projecting the joint density onto the real line leads to the derivation of a random three-term recurrence for polynomials with zeros distributed according to the circular Jacobi beta-ensemble.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0505552
dc.identifierhttp://arxiv.org/abs/math/0505552
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75317
dc.subjectProbability
dc.titleJacobians and rank 1 perturbations relating to unitary Hessenberg matrices
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