Anderson localization for radial tree graphs with random branching numbers

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2019
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Elsevier
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We 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.

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Damanik, David and Sukhtaiev, Selim. "Anderson localization for radial tree graphs with random branching numbers." Journal of Functional Analysis, 277, no. 2 (2019) Elsevier: 418-433. https://doi.org/10.1016/j.jfa.2018.11.007.

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