{"paper":{"title":"Heavy tails and one-dimensional localization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael Cranston, Nicola Squartini, Stanislav Molchanov","submitted_at":"2015-11-04T16:54:41Z","abstract_excerpt":"We address the fundamental questions concerning the operator \\begin{eqnarray*} H^{\\theta_0}\\psi(x)=-\\psi\"(x)+V(x,\\omega)\\psi(x),\\,\\psi(0)\\cos\\theta_0-\\psi'(0)\\sin\\theta_0=0. \\end{eqnarray*} where the random potential $V$ has a variety of forms. In one example, it is composed of width one bumps of random heights where the square root of the heights are in the domain of attraction of a stable law with index $\\alpha\\in(0,1)$ or in another it is composed of width one bumps of height one where the distance between bumps is in the domain of attraction of a stable law with index $\\alpha\\in(0,1).$ We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01394","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"}