{"paper":{"title":"How large is large? Estimating the critical disorder for the Anderson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"Jeffrey Schenker","submitted_at":"2013-05-30T01:32:22Z","abstract_excerpt":"Complete localization is shown to hold for the $d$-dimensional Anderson model with uniformly distributed random potentials provided the disorder strength $\\lambda >\\lambda_{And}$ where $\\lambda_{\\text{And}}$ satisfies $\\lambda_{\\text{And}}=\\mu_d e \\ln \\lambda_{\\text{And}}$ with $\\mu_d$ the self-avoiding walk connective constant for the lattice $\\mathbb{Z}^d$. Notably $\\lambda_{\\text{And}}$ is precisely the large disorder threshold proposed by Anderson in 1958."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6987","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}