A Geometric Approach to Absolutely Continuous Spectrum for Discrete Schrodinger Operators

被引：0

作者：

Froese, Richard ^{[1
]}

Hasler, David ^{[2
]}

Spitzer, Wolfgang ^{[3
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC, Canada

[2] Coll William & Mary, Dept Math, Williamsburg, VA USA

[3] Fern Univ Hagen, Fac Math & Comp Sci, Hagen, Germany

来源：

RANDOM WALKS, BOUNDARIES AND SPECTRA | 2011年 / 64卷

关键词：

Absolutely continuous spectrum; transfer matrices; hyperbolic geometry; tree graphs; ANDERSON MODEL; LARGE DISORDER; TREE GRAPHS; LATTICE;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We review a geometric approach to proving absolutely continuous (ac) spectrum for random and deterministic Schrodinger operators developed in [9-12]. We study decaying potentials in one dimension and present a simplified proof of ac spectrum of the Anderson model on trees. The latter implies ac spectrum for a percolation model on trees. Finally, we introduce certain loop tree models which lead to some interesting open problems.

引用

页码：201 / +

页数：3

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