Joint IAS/Princeton University Mathematical Physics Seminar

Characteristic Polynomials of the Hermitian Wigner and Sample Covariance Matrices

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.

Date & Time

November 01, 2011 | 4:30pm – 5:30pm

Location

S-101

Speakers

Tatyana Shcherbina

Affiliation

Institute for Low Temperature Physics, Kharkov

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