an:06599194
Zbl 1343.15024
del Molino, Luis Carlos Garc??a; Pakdaman, Khashayar; Touboul, Jonathan; Wainrib, Gilles
The real Ginibre ensemble with \(k=O(n)\) real eigenvalues
EN
J. Stat. Phys. 163, No. 2, 303-323 (2016).
00355137
2016
j
15B52 60F10 60B20 15A18
real Ginibre matrices; large deviations; log-gas; random matrices; joint eigenvalue density; spectral measure; asymptotic expansion
The authors consider the ensemble of real Ginibre matrices conditioned to have positive fraction \(\alpha >0\) of real eigenvalues. They 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 they provide an asymptotic expansion for the probability \(p_{\alpha n}^n\) that an \(n\times n\) Ginibre matrix has \(k=\alpha n\) real eigenvalues and then they characterize the spectral measures of these matrices.
Andreas Arvanitoyeorgos (Patras)