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arXiv · 1505.06527

Poisson statistics for random deformed band matrices with power law band width

Vladimir Pchelin
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Abstract

We show Poisson statistics for random band matrices which diagonal entries have Gaussian components. These components are possibly as small as $n^{-\varepsilon}$. Particularly, our result is applicable for a band matrix cut from the GUE with the band width satisfying $w^{3.5}<<n$. A uniform upper bound of the averaged density of states (DOS) is obtained for complex deformed Gaussian band matrices with arbitrary $w$. A lower estimate of the DOS is also proven for arbitrary $w$ in a certain class of band matrices.

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Vladimir Pchelin. 2015-06-01. Poisson statistics for random deformed band matrices with power law band width. https://arxiv.org/abs/1505.06527

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