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arXiv · 2609.30209

Localization near the edge for the lattice Anderson-Bernoulli model on general dimension

Linjun Li·Shihe Liu·Lingfu Zhang
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Abstract

The Anderson tight-binding model is a fundamental model of quantum transport and localization in disordered media. Completing 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.

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Linjun Li, Shihe Liu, Lingfu Zhang. 2026-09-24. Localization near the edge for the lattice Anderson-Bernoulli model on general dimension. https://arxiv.org/abs/2609.30209

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