English

Localization for non-stationary Anderson models in three dimensions

Mathematical Physics 2026-03-19 v1 math.MP Probability

Abstract

We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key inputs are a deterministic quantitative unique continuation theorem by Li and Zhang [Duke Math. J. 171(2): 327-415, 2022] and some combinatorial decompositions/bounds for non-stationary random potentials proved by the author [Commun. Math. Phys. 407:64, 2026].

Keywords

Cite

@article{arxiv.2603.17810,
  title  = {Localization for non-stationary Anderson models in three dimensions},
  author = {Omar Hurtado},
  journal= {arXiv preprint arXiv:2603.17810},
  year   = {2026}
}

Comments

22pp, comments welcome

R2 v1 2026-07-01T11:26:20.932Z