The real Ginibre ensemble with k = O(n) real eigenvalues
نویسندگان
چکیده
We consider the ensemble of real Ginibre matrices conditioned to have positive fraction α > 0 of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue density of such matrices and introduce a two phase log-gas whose stationary distribution coincides with the spectral measure of the ensemble. Using these tools we provide an asymptotic expansion for the probability pαn that an n× n Ginibre matrix has k = αn real eigenvalues and we characterize the spectral measures of these matrices.
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