Inter-relationships between orthogonal, unitary and symplectic matrix ensembles

Details Inter-relationships between orthogonal, unitary and symplectic matrix ensembles Inter-relationships between orthogonal, unitary and symplectic matrix ensembles

1999-07-07

arxiv.org/abs/solv-int/9907008v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

35 pages. Some results of the replaced preprint `Exact calculation of the distribution of every second eigenvalue in classical

Scientific paper

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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