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arXiv · cond-mat/9811142

Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges

P. J. Forrester·T. Nagao·G. Honner
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Abstract

For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion determinant. For the parameter dependent Gaussian and Laguerre ensembles the matrix elements of the determinant are expressed in terms of corresponding skew-orthogonal polynomials, and their limiting value for infinite matrix dimension are computed in the vicinity of the soft and hard edges respectively. A connection formula relating the distributions at the hard and soft edge is obtained, and a universal asymptotic behaviour of the two point correlation is identified.

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P. J. Forrester, T. Nagao, G. Honner. 1998-11-10. Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges. https://doi.org/10.1016/s0550-3213(99)00272-2

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