# King's College London

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

Research output: Contribution to journalArticle

Yan V Fyodorov, Jacek Grela, Eugene Strahov

Original language English Journal Of Physics A-Mathematical And Theoretical 51 13 5 Mar 2018 https://doi.org/10.1088/1751-8121/aaae2a E-pub ahead of print - 5 Mar 2018

## 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 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.

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