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arXiv · 1209.3385

On the second mixed moment of the characteristic polynomials of the 1D band matrices

Tatyana Shcherbina
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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 $< H_{ij}H_{lk}>=\delta_{ik}\delta_{jl}J_{ij}$, 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.

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Tatyana Shcherbina. 2012-09-15. On the second mixed moment of the characteristic polynomials of the 1D band matrices. https://arxiv.org/abs/1209.3385

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