Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles

Understand

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class.

• The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane.
• These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this.
• In the large $n$ limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble.