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.
Publié le : 2000-01-14
Classification:
Cheeger’s inequality,
spectral gap,
Neumann and Dirichlet eigenvalue,
jump process,
60J25,
60J75,
47A75
@article{1019160118,
author = {Chen, Mu-Fa and Wang, Feng-Yu},
title = {Cheeger's inequalities for general symmetric forms and existence
criteria for spectral gap},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 235-257},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160118}
}
Chen, Mu-Fa; Wang, Feng-Yu. Cheeger's inequalities for general symmetric forms and existence
criteria for spectral gap. Ann. Probab., Tome 28 (2000) no. 1, pp. 235-257. http://gdmltest.u-ga.fr/item/1019160118/