# Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Vi\'ete--Euler identity to Anderson localization

@article{Chulaevsky2016UniversalityOS, title={Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Vi\'ete--Euler identity to Anderson localization}, author={Victor Chulaevsky}, journal={arXiv: Mathematical Physics}, year={2016} }

It is shown that in a large class of disordered systems with non-degenerate disorder, in presence of non-local interactions, the Integrated Density of States (IDS) is at least H\"older continuous in one dimension and universally infinitely differentiable in higher dimensions. This result applies also to the IDS in any finite volume subject to the random potential induced by an ambient, infinitely extended disordered media. Dimension one is critical: in the Bernoulli case, within the class of…

## 3 Citations

### Density of States under non-local interactions II. Simplified polynomially screened interactions

- 2016

Mathematics

Following [5], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with…

### Density of States under non-local interactions III. N-particle Bernoulli--Anderson model

- 2017

Mathematics

Following [7,8], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with…

### Regularity of the Density of States of Random Schrödinger Operators

- 2020

Mathematics, Computer Science

Communications in Mathematical Physics

The proof of the Random Schrödinger operator case is an extensions of the proof for Anderson type models on ℓ2(G), showing that the Density of States is m times differentiable in the part of the spectrum where exponential localization is valid.

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