### Universality of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices

Shcherbina, T *(Institute for Advanced Study, Princeton)*

Thursday 20 September 2012, 11:10-11:50

Seminar Room 1, Newton Institute

#### Abstract

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices, i.e. of the hermitian matrices $H_n$ with independent Gaussian entries such that $\langle H_{ij}H_{lk}\rangle=\delta_{ik}\delta_{jl}J_{ij}$, where $J=(-W^2\triangle+1)^{-1}$. Assuming that $W^2=n^{1+\theta}$, $0<\theta<1$, we show that this asymptotic behavior (as $n\to\infty$) in the bulk of the spectrum coincides with those for the Gaussian Unitary Ensemble.

#### Presentation

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