A Riemann-Hilbert problem for skew-orthogonal polynomials

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dc.creatorPierce, V. U.
dc.date2006-10-19
dc.date2006-11-22
dc.date.accessioned2026-07-07T07:29:13Z
dc.date.available2026-07-07T07:29:13Z
dc.descriptionWe find a local $(d+1) \times (d+1)$ Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree $d$. Our Riemann-Hilbert problem is similar to a local $d \times d$ Riemann-Hilbert problem found by Kuijlaars and McLaughlin characterizing the bi-orthogonal polynomials. This gives more motivation for finding methods to compute asymptotics of high order Riemann-Hilbert problems, and brings us closer to finding asymptotics of the skew-orthogonal polynomials.
dc.description9 pages, v. 2 fixed some typos, v. 3 revised proof
dc.identifierhttps://arxiv.org/abs/math/0610592
dc.identifierhttp://arxiv.org/abs/math/0610592
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118022
dc.subjectComplex Variables
dc.subjectMathematical Physics
dc.subject15A52 (33C45; 82B31)
dc.titleA Riemann-Hilbert problem for skew-orthogonal polynomials
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