Year: 2015
Type: preprint
Abstract: We consider the ensemble of Real Ginibre matrices with a positive fraction $α>0$ of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue density of such matrices and we 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 $p^n_{αn}$ that an $n\times n$ Ginibre matrix has $k=αn$ real eigenvalues and we characterize the spectral measures of these matrices.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2225812598