1 February 2022 Anderson–Bernoulli localization on the three-dimensional lattice and discrete unique continuation principle
Linjun Li, Lingfu Zhang
Author Affiliations +
Duke Math. J. 171(2): 327-415 (1 February 2022). DOI: 10.1215/00127094-2021-0038


We consider the Anderson model with Bernoulli potential on the three-dimensional (3D) lattice Z3, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. We follow the framework of Bourgain–Kenig and Ding–Smart, and our main contribution is a 3D discrete unique continuation, which says that any eigenfunction of the harmonic operator with bounded potential cannot be too small on a significant fractional portion of all the points. Its proof relies on geometric arguments about the 3D lattice.


Download Citation

Linjun Li. Lingfu Zhang. "Anderson–Bernoulli localization on the three-dimensional lattice and discrete unique continuation principle." Duke Math. J. 171 (2) 327 - 415, 1 February 2022. https://doi.org/10.1215/00127094-2021-0038


Received: 18 September 2019; Revised: 30 July 2020; Published: 1 February 2022
First available in Project Euclid: 2 February 2022

MathSciNet: MR4375618
zbMATH: 1489.82044
Digital Object Identifier: 10.1215/00127094-2021-0038

Primary: 82B44
Secondary: 35J10 , 60H25 , 81Q10

Keywords: Anderson localization , Bernoulli potential , unique continuation , Wegner estimate

Rights: Copyright © 2022 Duke University Press

Vol.171 • No. 2 • 1 February 2022
Back to Top