Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices

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dc.creatorRosengren, Hjalmar
dc.date2006-06-16
dc.date2006-12-04
dc.date.accessioned2026-07-07T09:34:32Z
dc.date.available2026-07-07T09:34:32Z
dc.descriptionWe study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux) and number theory (representation of integers as sums of squares).
dc.descriptionThis is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math/0606391
dc.identifierhttp://arxiv.org/abs/math/0606391
dc.identifierSIGMA 2 (2006), 085, 12 pages
dc.identifierdoi:10.3842/SIGMA.2006.085
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159526
dc.subjectClassical Analysis and ODEs
dc.subjectCombinatorics
dc.subjectProbability
dc.subject15A15, 15A52, 42C05
dc.titleMultivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices
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