Density of States for Random Band Matrices in two dimensions

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 $W^{-2+\delta },$ where $\delta \to 0$ when $W\to \infty .$ The proof uses the supersymmetric approach and extends results by Disertori, Pinson and Spencer from three to two dimensions.

41 pages, 2 figures

References in corpus (2)

• Superbosonization of invariant random matrix ensembles
• Delocalization for a class of random block band matrices

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• The least singular value of the general deformed Ginibre ensemble
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