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Spectral statistics of random Schrödinger operator with growing potential (1506.07132v4)
Published 23 Jun 2015 in math.SP
Abstract: In this work we investigate the spectral statistics of random Schr\"{o}dinger operators $H\omega=-\Delta+\sum_{n\in\mathbb{Z}d}(1+|n|\alpha)q_n(\omega)|\delta_n\rangle\langle\delta_n|$, $\alpha>0$ acting on $\ell2(\mathbb{Z}d)$ where ${q_n}_{n\in\mathbb{Z}d}$ are i.i.d random variables distributed uniformly on $[0,1]$.