{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30209",
  "author_total": 3,
  "authors": [
    {
      "name": "Linjun Li"
    },
    {
      "name": "Shihe Liu"
    },
    {
      "name": "Lingfu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c601w786hf2t9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30209",
  "fulltext_url": null,
  "id": "c601w786hf2t9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30209",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214342689",
  "pdf_url": "https://arxiv.org/pdf/2609.30209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c601w786hf2t9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2609.30209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Localization near the edge for the lattice Anderson-Bernoulli model on general dimension",
  "title_text": "Localization near the edge for the lattice Anderson-Bernoulli model on general dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/c601w786hf2t9",
  "venue": "arXiv",
  "versions": []
}