English

Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap

Probability 2009-09-25 v1

Abstract

In this paper, some new forms of the Cheeger's inequalities are established for general (maybe unbounded) symmetric forms, the resulting estimates improve and extend the ones obtained by Lawler and Sokal (1988) for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are presented, based on the Cheeger's inequalities and a relationship between the spectral gap and the first Dirichlet and Neumann eigenvalues on local region.

Keywords

Cite

@article{arxiv.math/9804150,
  title  = {Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap},
  author = {Mu-Fa Chen and Feng-Yu Wang},
  journal= {arXiv preprint arXiv:math/9804150},
  year   = {2009}
}