Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 2, pp. 91-118   https://doi.org/10.15407/mag16.02.091     ( to contents , go back )
https://doi.org/10.15407/mag16.02.091

On the Correlation Functions of the Characteristic Polynomials of Real Random Matrices with Independent Entries

Ievgenii Afanasiev

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: afanasiev@ilt.kharkov.ua

Received February 28, 2020.

Abstract

The paper is concerned with the correlation functions of the characteristic polynomials of real random matrices with independent entries. The asymptotic behavior of the correlation functions is established in the form of a certain integral over unitary self-dual matrices with respect to the invariant measure. The integral is computed in the case of the second order correlation function. From the obtained asymptotics it is clear that the correlation functions behave like that for the Real Ginibre Ensemble up to a factor depending only on the fourth absolute moment of the common probability law of the matrix entries.

Mathematics Subject Classification 2000: 60B20, 15B52
Key words: random matrix theory, Ginibre ensemble, correlation functions of characteristic polynomials, moments of characteristic polynomials, SUSY

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