We prove decorrelation estimates for generalized lattice Anderson models on constructed with finite-rank perturbations in the spirit of Klopp . These are applied to prove that the local eigenvalue statistics and , associated with two energies and in the localization region and satisfying , are independent. That is, if are two bounded intervals, the random variables and , are independent and distributed according to a compound Poisson distribution whose Lévy measure has finite support. We also prove that the extended Minami estimate implies that the eigenvalues in the localization region have multiplicity at most the rank of the perturbation. The method of proof contains new ingredients that simplify the proof of the rank one case [12, 19, 21], extends to models for which the eigenvalues are degenerate, and applies to models for which the potential is not sign definite  in dimensions .
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Peter D. Hislop, Maddaly Krishna, Christopher Shirley, Decorrelation estimates for random Schrödinger operators with non rank one perturbations. J. Spectr. Theory 11 (2021), no. 1, pp. 63–89DOI 10.4171/JST/336