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Digitale Medien

Classical Skew Orthogonal Polynomials and Random Matrices (2000)

Adler, M. ; Forrester, P. J. ; Nagao, T. ; [weitere]

Springer

Journal of statistical physics 99 (2000), S. 141-170

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Details

ISSN: 1572-9613

Schlagwort(e): random matrices ; correlation functions ; orthogonal polynomials

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: 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 case 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1018644606835

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