{"paper":{"title":"Szeg\\\"o-type Theorems for One-Dimensional Schrodinger Operator with Random Potential (smooth case)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"L. Pastur, M. Shcherbina","submitted_at":"2018-09-13T07:42:43Z","abstract_excerpt":"The paper is a continuation of work [15] in which the general setting for analogs of the Szeg\\\"o theorem for ergodic operators was given and several interesting cases were considered. Here we extend the results of [15] to a wider class of test functions and symbols which determine the Szeg\\\"o-type asymptotic formula for the one-dimensional Schrodinger operator with random potential. We show that in this case the subleading term of the formula is given by a Central Limit Theorem in the spectral context, hence the term is asymptotically proportional to $L^{1/2}$, where $L$ is the length of the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04813","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"}