{"paper":{"title":"Localization for alloy-type models with non-monotone potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Martin Tautenhahn","submitted_at":"2012-11-16T13:55:06Z","abstract_excerpt":"We consider a family of self-adjoint operators [H_\\omega = - \\Delta + \\lambda V_\\omega, \\quad \\omega \\in \\Omega = \\bigtimes_{k \\in \\ZZ^d} \\RR,] on the Hilbert space $\\ell^2 (\\ZZ^d)$ or $L^2 (\\RR^d)$. Here $\\Delta$ denotes the Laplace operator (discrete or continuous), $V_\\omega$ is a multiplication operator given by the function $$V_\\omega (x) = \\sum_{k \\in \\ZZ^d} \\omega_k u(x-k) on $\\ZZ^d$, or \\quad V_\\omega (x) = \\sum_{k \\in \\ZZ^d} \\omega_k U(x-k) on $\\RR^d$,$$ and $\\lambda > 0$ is a real parameter modeling the strength of the disorder present in the model. The functions $u:\\ZZ^d \\to \\RR$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3891","kind":"arxiv","version":1},"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"}