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MPA

Seminar

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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