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arXiv · 1912.05254

Spectral fluctuations for Schr\"odinger operators with a random decaying potential

Jonathan Breuer·Yoel Grinshpon·Moshe White
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Abstract

We study fluctuations of polynomial linear statistics for discrete Schr\"odinger operators with a random decaying potential. We describe a decomposition of the space of polynomials into a direct sum of three subspaces determining the growth rate of the variance of the corresponding linear statistic. In particular, each one of these subspaces defines a unique critical value for the decay-rate exponent, above which the random variable has a limit that is sensitive to the underlying distribution and below which the random variable has asymptotically Gaussian fluctuations.

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Jonathan Breuer, Yoel Grinshpon, Moshe White. 2019-12-11. Spectral fluctuations for Schr\"odinger operators with a random decaying potential. https://arxiv.org/abs/1912.05254

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