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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/4263

Title: Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles
Authors: Akemann, G
Bender, M
Publication Date: 2010
Publisher: arXiv
Citation: arXiv:1003.4222v1
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.
URI: http://de.arxiv.org/abs/1003.4222
http://bura.brunel.ac.uk/handle/2438/4263
Appears in Collections:School of Information Systems, Computing and Mathematics Research Papers
Mathematical Physics

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