ISSN:
1572-9613
Keywords:
random matrices
;
correlation functions
;
orthogonal polynomials
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018644606835
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