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

Abstract

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. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes its structure as a one-parameter deformation of the Airy kernel more transparent.

21 pages

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Cited by in corpus (8)

• Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble
• A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
• The Elliptic Ginibre Ensemble: A Unifying Approach to Local and Global Statistics for Higher Dimensions
• Directional Extremal Statistics for Ginibre Eigenvalues
• Wronskian structures of planar symplectic ensembles
• Edge Behavior of Higher Complex-Dimensional Determinantal Point Processes
• Gegenbauer and other planar orthogonal polynomials on an ellipse in the complex plane
• Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics