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

Yan V. Fyodorov; Jacek Grela; Eugene Strahov

doi:10.1088/1751-8121/aaae2a

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

Yan V. Fyodorov, Jacek Grela, Eugene Strahov

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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
Article number	134003
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	51
Issue number	13
DOIs	https://doi.org/10.1088/1751-8121/aaae2a
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

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10.1088/1751-8121/aaae2a

Cite this

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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.",

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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.

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

Abstract

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Keywords

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