Asymptotic form of the density profile for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry

Abstract

In a recent study we have obtained correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in the bulk and at the soft edge of the spectrum. In the present study these results are used to similarly analyze the eigenvalue density for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry. As in the case of unitary symmetry, a matching is exhibited between the asymptotic expansion of the bulk density, expanded about the edge, and the asymptotic expansion of the edge density, expanded into the bulk. In addition, aspects of the asymptotic expansion of the smoothed density, which involves delta functions at the endpoints of the support, are interpreted microscopically.

arXiv comment28 pages, 1 figure

References in corpus (4)

• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• Classical skew orthogonal polynomials and random matrices
• Asymptotic corrections to the eigenvalue density of the GUE and LUE
• Exact Density of States for finite Gaussian Random Matrix Ensembles via Supersymmetry

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• Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities