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arXiv · 1606.09387

Density of States for Random Band Matrices in two dimensions

Margherita Disertori·Mareike Lager
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Abstract

We consider a two dimensional random band matrix ensemble, in the limit of infinite volume and fixed but large band width $W$. For this model we rigorously prove smoothness of the averaged density of states. We also prove that the resulting expression coincides with Wigner's semicircle law with a precision $W^{-2+δ},$ where $δ\to 0$ when $W\to \infty.$ The proof uses the supersymmetric approach and extends results by Disertori, Pinson and Spencer from three to two dimensions.

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BibTeXRIS

Margherita Disertori, Mareike Lager. 2017-04-28. Density of States for Random Band Matrices in two dimensions. https://doi.org/10.1007/s00023-017-0572-3

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