Eigenvalue correlations in non-Hermitean symplectic random matrices. (English) Zbl 1040.82028
Summary: A correlation function of complex eigenvalues of \(N \times N\) random matrices drawn from non-Hermitian random matrix ensembles of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are studied in detail in the regimes of weak and strong non-Hermiticity.
MSC:
82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
15B52 | Random matrices (algebraic aspects) |
33C90 | Applications of hypergeometric functions |
82B10 | Quantum equilibrium statistical mechanics (general) |