Browsing by Author "Sukhtaiev, Selim"
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Item Anderson localization for radial tree graphs with random branching numbers(Elsevier, 2019) Damanik, David; Sukhtaiev, SelimWe prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-lineᅠJacobi matricesᅠwhose entries are non-degenerate, independent, identically distributed random variables with singular distributions.Item Random Hamiltonians with arbitrary point interactions in one dimension(Elsevier, 2021) Damanik, David; Fillman, Jake; Helman, Mark; Kesten, Jacob; Sukhtaiev, SelimWe 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.