The chiral Gaussian two-matrix ensemble of real asymmetric matrices

Understand

We solve a family of Gaussian two-matrix models with rectangular Nx(N+v) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter mu.

• Our model can be thought of as the chiral extension of the real Ginibre ensemble, relevant for Dirac operators in the same symmetry class.
• It has the property that its eigenvalues are either real, purely imaginary, or come in complex conjugate eigenvalue pairs.
• The eigenvalue joint probability distribution for our model is explicitly computed, leading to a non-Gaussian distribution including K-Bessel functions.