Abstract:
Poissonian local eigenvalue statistics are believed to be a characteristic feature of spectrally localized quantum mechanical systems. For localized random Schrödinger operators Poissonian level statistics have however only been proven for the lattice Anderson model and close relatives: The proof of a key ingredient, the Minami estimate, crucially relied on the rank-1 character of the single-site potential. We present a more flexible approach towards Minami’s estimate, which for instance works at the bottom of the spectrum of a continuum random Schrödinger operator with sufficiently regular single-site distributions. The talk is based on joint work with Alex Elgart.