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

P Forrester, N Frankel, Tim Garoni

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

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 NxN 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
Original languageEnglish
Pages (from-to)023301-1 - 023301-26
Number of pages26
JournalJournal of Mathematical Physics
Volume47
Issue number2
DOIs
Publication statusPublished - 2006
Externally publishedYes

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