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A Riemann–Hilbert problem for skew-orthogonal polynomials

✍ Scribed by Virgil U. Pierce

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
191 KB
Volume
215
Category
Article
ISSN
0377-0427

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✦ Synopsis

We find a local (d + 1) × (d + 1) Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of orthogonal ensembles of random matrices with a potential function of degree d. Our Riemann-Hilbert problem is similar to a local d × 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 full asymptotic expansions of the skew-orthogonal polynomials.

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