Cheeger inequalities for unbounded graph Laplacians

被引：30

作者：

Bauer, Frank ^{[1
,2
]}

Keller, Matthias ^{[3
,4
]}

Wojciechowski, Radoslaw K. ^{[5
,6
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[3] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

[4] Univ Jena, Math Inst, D-07743 Jena, Germany

[5] CUNY York Coll, Jamaica, NY 11451 USA

[6] CUNY, Grad Ctr, New York, NY 10016 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2015年 / 17卷 / 02期

基金：

欧洲研究理事会;

关键词：

Isoperimetric inequality; intrinsic metric; Schrodinger operators; weighted graphs; curvature; volume growth; STOCHASTIC COMPLETENESS; ISOPERIMETRIC-INEQUALITIES; ESSENTIAL SPECTRUM; DIRICHLET FORMS; VOLUME GROWTH; INFINITE; CURVATURE; CONSTANT; SPACES; BOUNDS;

D O I：

10.4171/JEMS/503

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

引用

页码：259 / 271

页数：13

共 51 条

[1] LAMBDA-1, ISOPERIMETRIC-INEQUALITIES FOR GRAPHS, AND SUPERCONCENTRATORS [J].

ALON, N ;

MILMAN, VD .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1985, 38 (01) :73-88

[2]

[Anonymous], 1997, CBMS Regional Conference Series in Mathematics

[3]

[Anonymous], 2011, Ph.D. thesis

[4]

[Anonymous], 1986, Pitman Res. Notes Math. Ser

[5] THE NORMALIZED GRAPH CUT AND CHEEGER CONSTANT: FROM DISCRETE TO CONTINUOUS [J].

Arias-Castro, Ery ;

Pelletier, Bruno ;

Pudlo, Pierre .

ADVANCES IN APPLIED PROBABILITY, 2012, 44 (04) :907-937

[6] The dual Cheeger constant and spectra of infinite graphs [J].

Bauer, Frank ;

Hua, Bobo ;

Jost, Juergen .

ADVANCES IN MATHEMATICS, 2014, 251 :147-194

[7] THE SPECTRAL-RADIUS OF INFINITE-GRAPHS [J].

BIGGS, NL ;

MOHAR, B ;

SHAWETAYLOR, J .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1988, 20 :116-120

[8] SPECTRAL ANALYSIS OF CERTAIN SPHERICALLY HOMOGENEOUS GRAPHS [J].

Breuer, Jonathan ;

Keller, Matthias .

OPERATORS AND MATRICES, 2013, 7 (04) :825-847

[9]

Cheeger J., 1970, PROBLEMS ANAL, P195

[10]

Chung F., 2000, COMMUN ANAL GEOM, V8, P969

← 1 2 3 4 5 6 →