On characteristic polynomials for a generalized chiral random matrix ensemble with a source

Abstract

We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a $N\times N$ random matrix taken from a $L$-deformed Chiral Gaussian Unitary Ensemble with an external source $\Omega$. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Y.V. Fyodorov 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.

published version

References in corpus (2)

• On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
• Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices

Cited by in corpus (10)

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• Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
• Universal eigenvector correlations in quaternionic Ginibre ensembles
• On the moments of characteristic polynomials
• Averages of products and ratios of characteristic polynomials in polynomial ensembles
• Determinantal structure and bulk universality of conditional overlaps in the complex Ginibre ensemble
• Symmetric Function Theory and Unitary Invariant Ensembles
• Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature