On the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices

摘要

We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices H_n=n~(-1)A_(m,n) * A_(m,n), where A_(m,n) is a m × n complex random matrix with independent and identically distributed entries Ra_(αj) and Ia_(αj). We show that for the correlation function of any even order the asymptotic behavior in the bulk and at the edge of the spectrum coincides with those for the Gaussian Unitary Ensemble up to a factor, depending only on the fourth moment of the common probability law of entries Ra_(αj) and Ia_(αj), i.e., the higher moments do not contribute to the above limit.