Spectral Fluctuations for Schrödinger Operators with a Random Decaying Potential

Jonathan Breuer, Yoel Grinshpon*, Moshe J. White

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study fluctuations of polynomial linear statistics for discrete Schrödinger 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.

Original languageAmerican English
Pages (from-to)3763-3794
Number of pages32
JournalAnnales Henri Poincare
Volume22
Issue number11
DOIs
StatePublished - Nov 2021

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

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