Year: 2026
Type: preprint
Abstract: The Anderson tight-binding model is a fundamental model of quantum transport and localization in disordered media. Solving a problem left open by Bourgain and Kenig, this paper proves Anderson localization near the bottom of the spectrum for the lattice Anderson model with Bernoulli potential, in any dimension $d\ge 2$. The proof uses the multiscale framework of Fröhlich-Spencer and Bourgain-Kenig, and the main new ingredient is a probabilistic discrete unique continuation principle (PDUC) for the discrete Schrödinger equation. This PDUC is established via a bootstrap argument and a key probabilistic lemma proved by adaptively revealing the random potential.
Source: arXiv (Cornell University)
Authors: Li, Linjun, Liu, Shihe, Zhang, Lingfu
Institutions: University of Pennsylvania, Peking University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214342689