{"paper":{"title":"On nonlinear Schr\\\"odinger equations with random potentials: existence and probabilistic properties","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Leandro Cioletti, Lucas C. F. Ferreira, Marcelo Furtado","submitted_at":"2013-04-09T02:32:15Z","abstract_excerpt":"In this paper we are concerned with nonlinear Schr\\\"odinger equations with random potentials. Our class includes continuum and discrete potentials. Conditions on the potential $V_{\\omega}$ are found for existence of solutions almost sure $\\omega $. We study probabilistic properties like central limit theorem and law of larger numbers for the obtained solutions by independent ensembles. We also give estimates on the expected value for the $L^{\\infty}$-norm of the solution showing how it depends on the size of the potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2449","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"}