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|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - 5 Mar 2018|
Bibliographical noteFunding 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.
© 2018 IOP Publishing Ltd.
- Ginibre ensemble
- chiral unitary ensemble
- random characteristic polynomials