Corpus ID: 184487186

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}
}
  • Linjun Li, Ling-fu Zhang
  • Published 2019
  • Mathematics, Physics
  • arXiv: Analysis of PDEs
  • 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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