On the correlation functions of the characteristic polynomials of real random matrices with independent entries

Ievgenii Afanasiev

Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 2, pp. 91-118

Résumé

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.

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