Archive ouverte HAL – On characteristic polynomials for a generalized chiral random matrix ensemble with a source

Yan FyodorovJacek Grela 1 Eugene Strahov

J.Phys.A, 2018, 51 (13), pp.134003. 〈10.1088/1751-8121/aaae2a〉

We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques