Uniform Existence of the Integrated Density of States for Randomly Weighted Hamiltonians on Long-Range Percolation Graphs

被引：2

作者：

Ayadi, Slim ^{[1
]}

Schwarzenberger, Fabian ^{[2
]}

Veselic, Ivan ^{[2
]}

机构：

[1] Univ Tunis El Manar, Dept Math, Fac Sci Tunis, Tunis 2092, Tunisia

[2] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2013年 / 16卷 / 04期

关键词：

Spectral theory; Integrated density of states; Long-range percolation; SPECTRAL ASYMPTOTICS; RANDOM MATRICES; CONTINUITY; LAPLACIAN; OPERATORS;

D O I：

10.1007/s11040-013-9133-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider random Hamiltonians defined on long-range percolation graphs over Z(d). The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula.

引用

页码：309 / 330

页数：22

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