Finite size corrections for real eigenvalues of the elliptic Ginibre matrices

Abstract

We consider the elliptic Ginibre matrices in the orthogonal symmetry class that interpolates between the real Ginibre ensemble and the Gaussian orthogonal ensemble. We obtain the finite size corrections of the real eigenvalue densities in both the global and edge scaling regimes, as well as in both the strong and weak non-Hermiticity regimes. Our results extend and provide the rate of convergence to the previous recent findings in the aforementioned limits. In particular, in the Hermitian limit, our results recover the finite size corrections of the Gaussian orthogonal ensemble established by Forrester, Frankel and Garoni.

27 pages, 3 figures

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Cited by in corpus (3)

• Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge
• Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities
• The probability of almost all eigenvalues being real for the elliptic real Ginibre ensemble