A Riemann–Hilbert problem for skew-orthogonal polynomials

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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Journal of computational and applied mathematics Ročník 215; číslo 1; s. 230 - 241
Hlavní autor: Pierce, Virgil U.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 15.05.2008
Elsevier
Témata:
Exact sciences and technology
Fourier analysis
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Riemann–Hilbert problems
Sciences and techniques of general use
Skew-orthogonal polynomials
Special functions
Skew-orthogonal polynomials
Riemann–Hilbert problems
Polynomial function
Partition
Numerical analysis
Asymptotic expansion
Riemann problem
Riemann-Hilbert problems
Applied mathematics
Asymptotic approximation
Orthogonal polynomial
ISSN:0377-0427, 1879-1778
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2007.04.006