On the Second Mixed Moment of the Characteristic Polynomials of 1D Band Matrices |
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Authors: | Tatyana Shcherbina |
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Institution: | 1. Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA
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Abstract: | We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1D Gaussian band matrices, i.e., of the Hermitian N × N matrices H N with independent Gaussian entries such that 〈H ij H lk 〉 = δ ik δ jl J ij , where ${J=(-W^2\triangle+1)^{-1}}$ . Assuming that ${W^2=N^{1+\theta}}$ , ${0 < \theta \leq 1}$ , we show that the moment’s asymptotic behavior (as ${N\to\infty}$ ) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble. |
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