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

Research output: Contribution to journalArticlepeer-review

Yan V Fyodorov, Jacek Grela, Eugene Strahov

Original languageEnglish
JournalJournal Of Physics A-Mathematical And Theoretical
Issue number13
Early online date5 Mar 2018
Accepted/In press9 Feb 2018
E-pub ahead of print5 Mar 2018


King's Authors


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.

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