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 $k$-point distributions for the decimated orthogonal ensembles.

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

References in corpus (4)

• Level-Spacing Distributions and the Airy Kernel
• Biorthogonal ensembles
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• Classical skew orthogonal polynomials and random matrices

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• Growth models, random matrices and Painleve transcendents
• Local Central Limit Theorem for Determinantal Point Processes
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlevé Representations II
• Eigenvalue variance bounds for Wigner and covariance random matrices
• Painlevé expressions for LOE, LSE and interpolating ensembles
• A Note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices