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

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

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Tatyana Shcherbyna , Institute for Advanced Study
Fine Hall 601

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices. Assuming that the width of the band grows faster than $\sqrt{N}$, where $N$ is a matrix size, we show that this asymptotic behavior in the bulk of the spectrum coincides with those for the Gaussian Unitary or Orthogonal Ensemble.