A Generalisation of Dyson's Integration Theorem for Determinants

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dc.creatorAkemann, Gernot
dc.creatorShifrin, Leonid
dc.date2007-05-17
dc.date2007-07-06
dc.date.accessioned2026-07-07T10:35:54Z
dc.date.available2026-07-07T10:35:54Z
dc.descriptionDyson's integration theorem is widely used in the computation of eigenvalue correlation functions in Random Matrix Theory. Here we focus on the variant of the theorem for determinants, relevant for the unitary ensembles with Dyson index beta = 2. We derive a formula reducing the (n-k)-fold integral of an n x n determinant of a kernel of two sets of arbitrary functions to a determinant of size k x k. Our generalisation allows for sets of functions that are not orthogonal or bi-orthogonal with respect to the integration measure. In the special case of orthogonal functions Dyson's theorem is recovered.
dc.description7 pages, Latex. v2: typos corrected + reference added. v3: degenerate case added, to be published in J.Phys.A FTC
dc.identifierhttps://arxiv.org/abs/0705.2555
dc.identifierhttp://arxiv.org/abs/0705.2555
dc.identifierJ.Phys.A40:F785-F792,2007
dc.identifierdoi:10.1088/1751-8113/40/32/F01
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/179877
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.titleA Generalisation of Dyson's Integration Theorem for Determinants
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