The dual Cheeger constant and spectra of infinite graphs

被引：25
|
作者：
Bauer, Frank [1 ,2 ]
Hua, Bobo [2 ]
Jost, Juergen [2 ,3 ,4 ]
机构：
[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
[2] Max Planck Inst Math Sci, D-04103 Leipzig, Germany
[3] Univ Leipzig, Dept Math & Comp Sci, D-04109 Leipzig, Germany
[4] Santa Fe Inst Sci Complex, Santa Fe, NM 87501 USA
来源：
ADVANCES IN MATHEMATICS | 2014年 / 251卷
基金：
欧洲研究理事会;
关键词：
Discrete Laplace operator; Spectrum; Dual Cheeger constant; Infinite graph; EIGENVALUE COMPARISON-THEOREMS; NONCOMPACT MANIFOLDS; RANDOM-WALKS; DISCRETE; INEQUALITY; SUBGRAPHS; LAPLACIAN; GROWTH; VOLUME;
D O I：
10.1016/j.aim.2013.10.021
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we study the top of the spectrum of the normalized Laplace operator on infinite graphs. We introduce the dual Cheeger constant and show that it controls the top of the spectrum from above and below in a similar way as the Cheeger constant controls the bottom of the spectrum. Moreover, we show that the dual Cheeger constant at infinity can be used to characterize that the essential spectrum of the normalized Laplace operator shrinks to one point. (C) 2013 Elsevier Inc. All rights reserved.
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页码：147 / 194
页数：48
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