Inter-relationships between orthogonal, unitary and symplectic matrix ensembles
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 -point distributions for the decimated orthogonal ensembles.
Cite
@article{arxiv.solv-int/9907008,
title = {Inter-relationships between orthogonal, unitary and symplectic matrix ensembles},
author = {P. J. Forrester and E. M. Rains},
journal= {arXiv preprint arXiv:solv-int/9907008},
year = {2007}
}
Comments
35 pages. Some results of the replaced preprint `Exact calculation of the distribution of every second eigenvalue in classical random matrix ensembles with orthogonal symmetry' by PJF have been combined with new results of EMR to form the present article