We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies. All results are proved under the minimal hypothesis on the type of disorder: the random variables generating the trees assume at least two distinct values. This level of generality, in particular, allows us to treat radial trees with disordered geometry as well as Schrödinger operators with Bernoulli-type singular potentials. Our methods are based on an interplay between graph-theoretical properties of radial trees and spectral analysis of the associated random differential and difference operators on the half-line.

中文翻译：

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Anderson 模型在度量和离散树图上的定位

我们为度量和离散径向树上的几个 Anderson 模型建立了光谱和动态定位。定位结果是在包含在异常能量离散集的补充中的紧凑间隔上获得的。所有结果都在关于无序类型的最小假设下得到证明：生成树的随机变量至少假定两个不同的值。特别是，这种程度的一般性使我们能够处理具有无序几何的径向树以及具有伯努利型奇异势的薛定谔算子。我们的方法基于径向树的图论特性与半线上相关随机微分和差分算子的谱分析之间的相互作用。