Joint Princeton Mathematical Physics Seminar | |

Topic: | Characteristic Polynomials of the Hermitian Wigner and Sample Covariance Matrices |

Speaker: | Tatyana Shcherbina |

Affiliation: | Institute for Low Temperature Physics, Kharkov |

Date: | Tuesday, November 1 |

Time/Room: | 4:30pm - 5:30pm/S-101 |

Video Link: | https://video.ias.edu/joint/shcherbina |

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.