Spectral fluctuations for Schr\"odinger operators with a random decaying potential
Mathematical Physics
2019-12-12 v1 math.MP
Probability
Spectral Theory
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.
Cite
@article{arxiv.1912.05254,
title = {Spectral fluctuations for Schr\"odinger operators with a random decaying potential},
author = {Jonathan Breuer and Yoel Grinshpon and Moshe White},
journal= {arXiv preprint arXiv:1912.05254},
year = {2019}
}