{"arxiv_id":"1505.05218","incoming":{"papers":1,"sentences":1,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1809.01236","title":"Decorrelation estimates for random Schr\\\"odinger operators with non rank one perturbations","url":"/paper/1809.01236","section":"Contents","sentence":"This paper replaces the manuscript [ref] by the first two authors, completing and improving the arguments, and extending the results.","intent_p":0.88,"contests_p":null}]}],"unlabelled_sentences":0},"outgoing":{"papers":3,"sentences":11,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":2,"quotes":[{"arxiv_id":"1409.2328","title":"Eigenvalue statistics for random Schrodinger operators with non rank one perturbations","url":"/paper/1409.2328","section":"Asymptotic independence and decorrelation estimates","sentence":"The extended Minami estimate [ref] implies that we need to estimate: { (Tr E_H_ω,ℓ (I_L (E)) ≤m_k ) ∩(Tr E_H_ω,ℓ (J_L(E^')) ≤m_k ) } In fact, we consider the more general estimate: { (Tr E_H_ω,L (I_L(E)) = k_1 ) ∩(Tr E_H_ω,L (J_L(E^')) = k_2 ) }, where $k_1, k_2$ are positive integers independent of $L$.","intent_p":0.82,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":1,"sentences":2,"quotes":[{"arxiv_id":"1006.4427","title":"Spectral statistics for the discrete Anderson model in the localized regime","url":"/paper/1006.4427","section":"Asymptotic independence and decorrelation estimates","sentence":"We refer to [ref] for a description of the region of complete localization $Σ_CL$.","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":7},"claims":[{"relation":"same_result","label":"States the same result","papers":[{"arxiv_id":"1809.01236","url":"/paper/1809.01236","title":"Decorrelation estimates for random Schr\\\"odinger operators with non rank one perturbations","main_claim":"These are applied to prove that the local eigenvalue statistics $\\xi^\\omega_{E}$ and $\\xi^\\omega_{E^\\prime}$, associated with two energies $E$ and $E'$ in the localization region and satisfying $|E - E'| > 4d$, are independent.","p":0.81}]}],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1505.05218"}}