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...
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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 215; H. 1; S. 230 - 241 |
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| Sprache: | Englisch |
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Elsevier B.V
15.05.2008
Elsevier |
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Pierce, Virgil U. |
| Author_xml | – sequence: 1 givenname: Virgil U. surname: Pierce fullname: Pierce, Virgil U. email: vpierce@math.ohio-state.edu organization: Department of Mathematics, The Ohio State University, USA |
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| Cites_doi | 10.1155/S107379289900029X 10.1090/cln/003 10.1088/0305-4470/34/37/312 10.1016/S0550-3213(98)00501-X 10.1007/BF02099545 10.1016/S0167-2789(01)00173-7 10.5802/aif.2158 10.1016/j.aim.2003.08.015 10.1103/PhysRevLett.81.248 10.1016/j.jat.2006.05.006 10.1007/s11040-004-2719-y 10.1016/j.cam.2004.01.043 10.1007/s00220-003-0934-1 10.1002/(SICI)1097-0312(199911)52:11<1335::AID-CPA1>3.0.CO;2-1 10.1155/S1073792804132194 10.1023/A:1011457714198 10.1088/0305-4470/36/16/312 10.1023/A:1018644606835 10.1016/0196-8858(80)90008-1 10.1155/S1073792803211089 10.1017/CBO9780511791246 10.1002/(SICI)1097-0312(199912)52:12<1491::AID-CPA2>3.0.CO;2-# 10.1007/BF01208498 10.1023/A:1004516918143 10.1215/S0012-9074-02-11211-3 10.1016/S0550-3213(00)00448-X 10.1088/0305-4470/39/28/S02 |
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| Keywords | Skew-orthogonal polynomials Riemann–Hilbert problems Polynomial function Partition Numerical analysis Asymptotic expansion Riemann problem Riemann-Hilbert problems Applied mathematics Asymptotic approximation Orthogonal polynomial |
| Language | English |
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Riemann–Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of orthogonal... |
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| SubjectTerms | 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 |
| Title | A Riemann–Hilbert problem for skew-orthogonal polynomials |
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