标题： 绝对连续谱对于有限锥型树上的随机算子 显示英文标题

标题： Absolutely continuous spectrum for random operators on trees of finite cone type

摘要： 我们研究一类树上随机算子的谱。这些树具有有限多个锥类型，且可以通过替换规则构造。随机算子是拉普拉斯型算子的摄动，要么通过随机势，要么通过随机跳跃项，即对角线外元素的扰动。我们证明了对于足够小但广泛的无序性，绝对连续谱的任意大一部分是稳定的。 显示英文摘要

摘要： We study the spectrum of random operators on a large class of trees. These trees have finitely many cone types and they can be constructed by a substitution rule. The random operators are perturbations of Laplace type operators either by random potentials or by random hopping terms, i.e., perturbations of the off-diagonal elements. We prove stability of arbitrary large parts of the absolutely continuous spectrum for sufficiently small but extensive disorder.