Cheeger's Inequalities for General Symmetric Forms and Existence Criteria for Spectral Gap

In this paper, some new forms of Cheeger's inequalities are established for general (maybe unbounded) symmetric forms (Theorems 1.1 and 1.2): the resulting estimates improve and extend the ones obtained by Lawler and Sokal for bounded jump processes. Furthermore, some existence criteria for spe...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of probability 2000-01, Vol.28 (1), p.235-257
Main Authors: Chen, Mu-Fa, Wang, Feng-Yu
Format: Article
Language:English
Subjects:
47A75
60J25
60J75
Cheeger’s inequality
Eigenvalues
jump process
Markov chains
Markov processes
Mathematical inequalities
Neumann and Dirichlet eigenvalue
Radon
spectral gap
Spectral theory
Symmetry
Topological theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, some new forms of Cheeger's inequalities are established for general (maybe unbounded) symmetric forms (Theorems 1.1 and 1.2): the resulting estimates improve and extend the ones obtained by Lawler and Sokal for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are presented (Theorems 1.4 and 3.1), based on Cheeger's inequalities and a relationship between the spectral gap and the first Dirichlet and Neumann eigenvalues on local region.
ISSN:0091-1798
2168-894X
DOI:10.1214/aop/1019160118