{"paper":{"title":"A bound on the averaged spectral shift function and a lower bound on the density of states for random Schr\\\"odinger operators on $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abel Klein, Adrian Dietlein, Martin Gebert, Peter D. Hislop, Peter M\\\"uller","submitted_at":"2016-06-05T23:12:59Z","abstract_excerpt":"We obtain a bound on the expectation of the spectral shift function for alloy-type random Schr\\\"odinger operators on $\\mathbb{R}^d$ in the region of localisation, corresponding to a change from Dirichlet to Neumann boundary conditions along the boundary of a finite volume. The bound scales with the area of the surface where the boundary conditions are changed. As an application of our bound on the spectral shift function, we prove a reverse Wegner inequality for finite-volume Schr\\\"odinger operators in the region of localisation with a constant locally uniform in the energy. The application re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01579","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"}