## Abstract

We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a N × 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.

Original language | American English |
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Article number | 134003 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 51 |

Issue number | 13 |

DOIs | |

State | Published - 5 Mar 2018 |

### Bibliographical note

Funding Information:The research at King’s College London was supported by EPSRC grant EP/N009436/1 ‘The many faces of random characteristic polynomials’. JG acknowledges partial support from the National Science Centre, Poland under an agreement 2015/19/N/ST1/00878.

Publisher Copyright:

© 2018 IOP Publishing Ltd.

## Keywords

- Ginibre ensemble
- chiral unitary ensemble
- random characteristic polynomials