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

N1 - Publisher Copyright:
© 2018 IOP Publishing Ltd.

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 × 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 × 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.

KW - Ginibre ensemble

KW - chiral unitary ensemble

KW - random characteristic polynomials

UR - http://www.scopus.com/inward/record.url?scp=85043495870&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aaae2a

DO - 10.1088/1751-8121/aaae2a

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AN - SCOPUS:85043495870

SN - 1751-8113

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 13

M1 - 134003

ER -