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

Annals of Probability

Volumn 28, Issue 1, 2000, Pages 235-257

  Chen, Mu Fa ^a   Wang, Feng Yu ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Cheeger's inequality; Jump process; Neumann and Dirichlet eigenvalue; Spectral gap

Indexed keywords

EID: 0034336987     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1019160118     Document Type: Article

References (10)

1. BOBKOV, S. and LEDOUX, M. (1997). Poincaré inequalities and Talagrand's concentration phenomenon for the exponential distribution. Probab. Theory Related Fields 107 383-400
2. CHEEGER, J. (1970). A lower bound for the smallest eigenvalue of the Laplacian. In Problems in Analysis. A Symposium in Honor of S. Bochner (R. C. Gunning, ed.) 195-199. Princeton Univ. Press.
3. CHEN, M. F. (1992). From Markov Chains to Non-Equilibrium Particle Systems. World Scientific, Singapore
4. CHEN, M. F. (1996). Estimation of spectral gap for Markov chains. Acta Math. Sinica. (N. S.) 12 337-360
5. CHEN, M. F. and WANG, F. Y. (1997). Estimation of spectral gap for elliptic operators. Trans. Amer. Math. Soc. 349 1209-1237
6. CHUNG, F. R. K. (1997). Spectral Graph Theory. Amer. Math. Soc., Providence, RI.
7. FUKUSHIMA, M., OSHIMA, Y. and Takeda, M. (1994). Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Berlin.
8. 2 spectrum for Markov chain and Markov processes: a generalization of Cheeger's inequality. Trans. Amer. Math. Soc. 309 557-580
9. SALOFF-COSTE, L. (1997). Lectures on finite Markov chains. Lecture Notes in Math. 1665 301-413. Springer, Berlin.
10. WANG, F. Y. (1999). Existence of spectral gap for elliptic operators. Ark. Mat. 37 395-407.