Interrelationships between orthogonal, unitary and symplectic matrix ensembles. (English) Zbl 0987.15004
Bleher, Pavel (ed.) et al., Random matrix models and their applications. Based on talks and lectures from the workshop, Berkeley, CA, USA, February 22-26, 1999. Cambridge: Cambridge University Press. Math. Sci. Res. Inst. Publ. 40, 171-207 (2001).
Summary: 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 form a unitary ensemble. Also considered are the \(k\)-point distributions for the decimated orthogonal ensembles.
For the entire collection see [Zbl 0967.00059].
For the entire collection see [Zbl 0967.00059].
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A30 | Algebraic systems of matrices |
| 60B11 | Probability theory on linear topological spaces |
