Local eigenvalue statistics for higher-rank Anderson models after Dietlein-Elgart

We use the method of eigenvalue level spacing developed by Dietlein and Elgart [Level spacing and Poisson statistics for continuum random Schrodinger operators, J. Eur. Math. Soc. (JEMS) 23(4) (2021) 1257-1293] to prove that the local eigenvalue statistics (LES) for the Anderson model on d, with uniform higher-rank 2, single-site perturbations, is given by a Poisson point process with intensity measure n(E0)ds, where n(E0) is the density of states at energy E0 in the region of localization near the spectral band edges. This improves the result of Hislop and Krishna [Eigenvalue statistics for random Schrodinger operators with non-rank one perturbations, Comm. Math. Phys. 340(1) (2015) 125-143], who proved that the LES is a compound Poisson process with Levy measure supported on the set {1, 2,m}. Our proofs are an application of the ideas of Dietlein and Elgart to these higher-rank lattice models with two spectral band edges, and illustrate, in a simpler setting, the key steps of the proof of Dietlein and Elgart.