{"paper":{"title":"Decorrelation estimates for random Schr\\\"odinger operators with non rank one perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"M. Krishna, Peter D. Hislop","submitted_at":"2015-05-20T01:05:11Z","abstract_excerpt":"We prove decorrelation estimates for generalized lattice Anderson models on $Z^d$ constructed with finite-rank perturbations in the spirit of Klopp \\cite{klopp}. These are applied to prove that the local eigenvalue statistics $\\xi^\\omega_{E}$ and $\\xi^\\omega_{E^\\prime}$, associated with two energies $E$ and $E'$ satisfying $|E - E'| > 4d$, are independent. That is, if $I,J$ are two bounded intervals, the random variables $\\xi^\\omega_{E}(I)$ and $\\xi^\\omega_{E'}(J)$, are independent and distributed according to a compound Poisson distribution whose L\\'evy measure has finite support. We also pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05218","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"}