The probability of almost all eigenvalues being real for the elliptic real Ginibre ensemble

Gernot Akemann, Sung-Soo Byun, Yong-Woo Lee

We investigate real eigenvalues of real elliptic Ginibre matrices of size $n$, indexed by the parameter of asymmetry $\ddot{I}„\in [0,1]$. In both the strongly and weakly non-Hermitian re…