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

TY - JOUR

T1 - On characteristic polynomials for a generalized chiral random matrix ensemble with a source

AU - Fyodorov, Yan V

AU - Grela, Jacek

AU - Strahov, Eugene

PY - 2018/3/5

Y1 - 2018/3/5

N2 - 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.

AB - 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.

U2 - 10.1088/1751-8121/aaae2a

DO - 10.1088/1751-8121/aaae2a

M3 - Article

SN - 1751-8113

VL - 51

JO - Journal Of Physics A-Mathematical And Theoretical

JF - Journal Of Physics A-Mathematical And Theoretical

IS - 13

ER -