Characteristic polynomials of the hermitian Wigner and sample covariance matrices
Characteristic polynomials of the hermitian Wigner and sample covariance matrices

Tatyana Shcherbina, Institute for Low Temperature Physics, Kharkov, Ukraine
IAS Room S101
We consider asymptotics of the correlation functions of characteristic polynomials of the hermitian Wigner matrices $H_n=n^{1/2}W_n$ and the hermitian sample covariance matrices $X_n=n^{1}A_{m,n}^*A_{m,n}$. We use the integration over the Grassmann variables to obtain a convenient integral representation. Then we show that the asymptotics of the correlation functions of any even order coincide with that for the GUE up to a factor, depending only on the fourth moment of the common probability law of the matrix entries, i.e. that the higher moments do not contribute to the above asymptotics.