dorsal/arxiv
View SchemaClassical skew orthogonal polynomials and random matrices
| Authors | M. Adler, P. J. Forrester, T. Nagao, P. van Moerbeke |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9907001 |
| URL | https://arxiv.org/abs/solv-int/9907001 |
| DOI | 10.1023/A:1018644606835 |
Abstract
Skew orthogonal polynomials arise in the calculation of the $n$-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely determined by a certain sum involving the skew orthogonal polynomials. In the cases that the eigenvalue probability density function involves a classical weight function, explicit formulas for the skew orthogonal polynomials are given in terms of related orthogonal polynomials, and the structure is used to give a closed form expression for the sum. This theory treates all classical cases on an equal footing, giving formulas applicable at once to the Hermite, Laguerre and Jacobi cases.
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"abstract": "Skew orthogonal polynomials arise in the calculation of the $n$-point\ndistribution function for the eigenvalues of ensembles of random matrices with\northogonal or symplectic symmetry. In particular, the distribution functions\nare completely determined by a certain sum involving the skew orthogonal\npolynomials. In the cases that the eigenvalue probability density function\ninvolves a classical weight function, explicit formulas for the skew orthogonal\npolynomials are given in terms of related orthogonal polynomials, and the\nstructure is used to give a closed form expression for the sum. This theory\ntreates all classical cases on an equal footing, giving formulas applicable at\nonce to the Hermite, Laguerre and Jacobi cases.",
"arxiv_id": "solv-int/9907001",
"authors": [
"M. Adler",
"P. J. Forrester",
"T. Nagao",
"P. van Moerbeke"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1023/A:1018644606835",
"title": "Classical skew orthogonal polynomials and random matrices",
"url": "https://arxiv.org/abs/solv-int/9907001"
},
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