On the spectral Hausdorff dimension of 1D discrete Schr\"odinger operators under power decaying perturbations

  title={On the spectral Hausdorff dimension of 1D discrete Schr\"odinger operators under power decaying perturbations},
  author={Vanderl{\'e}a Rodrigues Baz{\~a}o and Silas L. Carvalho and C'esar R. de Oliveira},
  journal={arXiv: Mathematical Physics},
We show that spectral Hausdorff dimensional properties of discrete Schr\"oodinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component. 
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