# Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principle

@article{Li2019AndersonBernoulliLO, title={Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principle}, author={Linjun Li and Ling-fu Zhang}, journal={arXiv: Analysis of PDEs}, year={2019} }

We consider the Anderson model with Bernoulli potential on $\mathbb{Z}^{3}$, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. The proof follows the framework by Bourgain--Kenig and Ding--Smart. Our main contribution is the 3D discrete unique continuation, which says that any eigenfunction of harmonic operator with potential cannot be too small on a significant fractional portion of $\mathbb{Z}^{3}$.

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