{"paper":{"title":"The spectrum of the random environment and localization of noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"Balint Virag, Dimitrios Cheliotis","submitted_at":"2008-04-30T12:51:46Z","abstract_excerpt":"We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.4814","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"}