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

被引：21

作者：

Keller, Matthias ^{[1
]}

Lenz, Daniel ^{[1
]}

Warzel, Simone ^{[2
]}

机构：

[1] Univ Jena, Math Inst, D-07743 Jena, Germany

[2] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2012年 / 118卷

基金：

以色列科学基金会;

关键词：

RANDOM SCHRODINGER-OPERATORS; ANDERSON MODEL; BETHE LATTICE; RANDOM-WALKS; GRAPHS; LOCALIZATION; PERCOLATION;

D O I：

10.1007/s11854-012-0040-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：363 / 396

页数：34

共 27 条

[1]

Aizenman M., J EUROPEAN IN PRESS

[2] Stability of the absolutely continuous spectrum of random Schrodinger operators on tree graphs [J].