On the Correlation Functions of the Characteristic Polynomials of Random Matrices with Independent Entries: Interpolation Between Complex and Real Cases

Abstract: The paper is concerned with the correlation functions of the characteristic polynomials of random matrices with independent complex entries. We investigate how the asymptotic behavior of the correlation functions depends on the second moment of the common probability law of the matrix entries, a sort of ``reality measure'' of the entries. It is shown that the correlation functions behave like that for the Complex Ginibre Ensemble up to a factor depending only on the second moment and the fourth absolute moment of the common probability law of the matrix entries.