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On the Correlation Functions of the Characteristic Polynomials of Non-Hermitian Random Matrices with Independent Entries

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Abstract

The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for the Complex Ginibre Ensemble up to a factor depending only on the fourth absolute moment of the common probability law of the matrix entries.

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Notes

  1. Here and below we omit Z only if \(Z = {{\,\mathrm{diag}\,}}\{z_1, \ldots , z_m\}\).

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Acknowledgements

The author is grateful to Prof. M. Shcherbina for the statement of the problem and fruitful discussions.

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  1. B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine

    Ie. Afanasiev

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  1. Ie. Afanasiev
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Correspondence to Ie. Afanasiev.

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Communicated by Hal Tasaki.

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Supported in part by The President of Ukraine Grant and by the Akhiezer Foundation scholarship.

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Afanasiev, I. On the Correlation Functions of the Characteristic Polynomials of Non-Hermitian Random Matrices with Independent Entries. J Stat Phys 176, 1561–1582 (2019). https://doi.org/10.1007/s10955-019-02353-w

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  • DOI: https://doi.org/10.1007/s10955-019-02353-w

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