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  • 1
    Electronic Resource
    Electronic Resource
    Exact Wigner Surmise Type Evaluation of the Spacing Distribution in the Bulk of the Scaled Random Matrix Ensembles (2000)
    Springer
    Letters in mathematical physics 53 (2000), S. 195-200 
    Details
    ISSN: 1573-0530
    Keywords: random matrices ; Painlevé transcendents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices, respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s)e−b(s) for a simply related to a Painlevé transcendent and b its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011074616607
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Classical Skew Orthogonal Polynomials and Random Matrices (2000)
    Springer
    Journal of statistical physics 99 (2000), S. 141-170 
    Details
    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
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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