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Inter-relationships between orthogonal, unitary and symplectic matrix ensembles

P. J. Forrester·E. M. Rains
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Abstract

We consider the following problem: When do alternate eigenvalues taken from a matrix ensemble themselves form a matrix ensemble? More precisely, we classify all weight functions for which alternate eigenvalues from the corresponding orthogonal ensemble form a symplectic ensemble, and similarly classify those weights for which alternate eigenvalues from a union of two orthogonal ensembles forms a unitary ensemble. Also considered are the $k$-point distributions for the decimated orthogonal ensembles.

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P. J. Forrester, E. M. Rains. 1999-09-29. Inter-relationships between orthogonal, unitary and symplectic matrix ensembles. https://arxiv.org/abs/solv-int/9907008

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