Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs

被引：14

作者：

Muller, Peter ^{[1
]}

Stollmann, Peter

机构：

[1] Univ Gottingen, Inst Theoret Phys, D-37077 Gottingen, Germany

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

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2007年 / 252卷 / 01期

关键词：

laplacian; percolation; integrated density of states;

D O I：

10.1016/j.jfa.2007.06.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate Laplacians on supercritical bond-percolation graphs with different boundary conditions at cluster borders. The integrated density of states of the Dirichlet Laplacian is found to exhibit a Lifshits tail at the lower spectral edge, while that of the Neumann Laplacian shows a van Hove asymptotics, which results from the percolating cluster. At the upper spectral edge, the behaviour is reversed. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：233 / 246

页数：14

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