On characteristic polynomials for a generalized chiral random matrix ensemble with a source. (English) Zbl 1388.60025
Summary: 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 [the first author, “On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry”, Preprint, 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.
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