Damanik, DavidFillman, JakeHelman, MarkKesten, JacobSukhtaiev, Selim2021-03-122021-03-122021Damanik, David, Fillman, Jake, Helman, Mark, et al.. "Random Hamiltonians with arbitrary point interactions in one dimension." <i>Journal of Differential Equations,</i> 282, (2021) Elsevier: 104-126. https://doi.org/10.1016/j.jde.2021.01.044.https://hdl.handle.net/1911/110177We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we prove the following dichotomy: Either every realization of the random operator has purely absolutely continuous spectrum or spectral and exponential dynamical localization hold. In particular, we establish Anderson localization for Schrödinger operators with Bernoulli-type random singular potential and singular density.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.Journal articlehttps://doi.org/10.1016/j.jde.2021.01.044