{"paper":{"title":"The scaling limit of the critical one-dimensional random Schrodinger operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Balint Virag, Benedek Valko, Evgenij Kritchevski","submitted_at":"2011-07-15T12:45:49Z","abstract_excerpt":"We consider two models of one-dimensional discrete random Schrodinger operators (H_n \\psi)_l ={\\psi}_{l-1}+{\\psi}_{l +1}+v_l {\\psi}_l, {\\psi}_0={\\psi}_{n+1}=0 in the cases v_k=\\sigma {\\omega}_k/\\sqrt{n} and v_k=\\sigma {\\omega}_k/ \\sqrt{k}. Here {\\omega}_k are independent random variables with mean 0 and variance 1.\n  We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3058","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"}