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.
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页码：201 / +
页数：3
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