{"paper":{"title":"Groupoids, von Neumann Algebras and the Integrated Density of States","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"D. Lenz, I. Veseli\\'c, N. Peyerimhoff","submitted_at":"2002-03-16T15:19:04Z","abstract_excerpt":"We study spectral properties of random operators in the general setting of groupoids and von Neumann algebras. In particular, we establish an explicit formula for the canonical trace of the von Neumann algebra of random operators and define an abstract density of states.\n  The general setting applies to many examples studied before while we lay special emphasis on a new one: random Schr\\\"odinger operators on manifolds. In this case, we show that the distribution function of the abstract density of states coincides with the integrated density of states defined via an exhaustion procedure.\n  The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0203026","kind":"arxiv","version":2},"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"}