Smoothness of integrated density of states and level statistics of the Anderson model when single site distribution is convolution with the Cauchy distribution

Dhriti Ranjan Dolai

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arXiv · 2203.04569

Smoothness of integrated density of states and level statistics of the Anderson model when single site distribution is convolution with the Cauchy distribution

Dhriti Ranjan Dolai

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Abstract

In this work we consider the Anderson model on $\ell^2(\mathbb{Z}^d)$ when the single site distribution (SSD) is given by $μ_1 * μ_2$, where $μ_1$ is the Cauchy distribution and $μ_2$ is any probability measure. For this model we prove that the integrated density of states (IDS) is infinitely differentiable irrespective of the disorder strength. Also, we investigate the local eigenvalue statistics of this model in $d\ge 2$, without any assumption on the localization property.

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BibTeX RIS

Dhriti Ranjan Dolai. 2022-03-09. Smoothness of integrated density of states and level statistics of the Anderson model when single site distribution is convolution with the Cauchy distribution. https://arxiv.org/abs/2203.04569

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