{"paper":{"title":"An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schr\\\"{o}dinger operators","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fr\\'ed\\'eric Klopp (LAGA), Jean-Michel Combes (CPT), Peter Hislop","submitted_at":"2006-05-09T10:21:55Z","abstract_excerpt":"We prove that the integrated density of states (IDS) of random Schr\\\"{o}dinger operators with Anderson-type potentials on $L^2 (\\R^d)$, for $d \\geq1$, is locally H\\\"{o}lder continuous at all energies with the same H\\\"{o}lder exponent $0<\\alpha\\leq1$ as the conditional probability measure for the single-site random variable. As a special case, we prove that if the probability distribution is absolutely continuous with respect to Lebesgue measure with a bounded density, then the IDS is Lipschitz continuous at all energies. The single-site potential $u\\in L\\_0^\\infty (\\R^d)$ must be nonnegative a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0605029","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"}