Math Phys Seminar: Tatyana Shcherbina (Inst. for Low Temp. Phys., Kharkov, Ukraine) "Characteristic polynomials of the hermitian Wigner and sample co

Tue, Nov 1, 2011, 4:30 pm to 6:00 pm
Location: 
IAS Simonyi Hall 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.