Some Estimates Regarding Integrated density of States for Random Schr\"{o}dinger Operator with decaying Random Potentials

Dhriti Ranjan Dolai

Some Estimates Regarding Integrated density of States for Random Schr\"{o}dinger Operator with decaying Random Potentials

Spectral Theory 2015-06-26 v2

Authors: Dhriti Ranjan Dolai

Abstract

We investigate some bounds for the density of states in the pure point regime for the random Schr\"{o}dinger operators $H^{\omega}=-\Delta+\displaystyle\sum_{n\in\mathbb{Z}^d}a_nq_n(\omega)$ , acting on $\ell^2(\mathbb{Z}^d)$ , where $\{q_n\}$ are iid random variables and $a_n\simeq|n|^{-\alpha}~~\alpha>0$ .

Keywords

random Schrödinger operator integrated density of states pure point regime decaying random potentials independent identically distributed variables

Cite

@article{arxiv.1501.05055,
  title  = {Some Estimates Regarding Integrated density of States for Random Schr\"{o}dinger Operator with decaying Random Potentials},
  author = {Dhriti Ranjan Dolai},
  journal= {arXiv preprint arXiv:1501.05055},
  year   = {2015}
}

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