Estimate of exponential convergence rate in total variation by spectral gap

Acta Mathematica Sinica

Volumn 14, Issue 1, 1998, Pages 9-16

  Mufa, Chcn ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Markov procosses; Spectral gap; Variation

Indexed keywords

EID: 33746763549     PISSN: 10009574     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02563878     Document Type: Article

References (13)

1. Liggett T M. Exponential LI convergence of attractive reversible nearest particle systems. Ann Probab, 1989, 17: 403-432
2. Chcn M F. Exponential Z.2-convergence and L2-spectral gap for Markov processes. Acta Math Sin New Ser, 1991, 7(1): 19-37
3. Ch'en M F. From Markov Chains to Non-Equilibrium Particle Systems. Singapore: World Scientific, 1992
4. Chen M F. Estimation'of spectral gap for Markov chains. Acta Math Sin New-Ser, 1996,' 12(4): 337-360
5. Chen M F, Wang F Y. Estimation of spectral gap for elliptic operators. Trans Amer Math Soc, 1997, 349: 1239-1267
6. Chen M F, Wang F Y. General formula for lower bound of the first eigenvalue on Riemannian manifolds. Sei Sin 1997, 27(1): 34-42 (Chinese Edition); 1997, 40(4): 384-394 (English Edition)
7. Chen M F, Wang F Y. Estimation of the first eigenvalue of second order elliptic operators. J Funct Anal, 1995, 131(2): 345-363
8. Diaconis, Stroock. Geometric bounds for eigenvalues of Markov chains. Ann Appl Prob, 1991, 1(1): 36-61
9. Diaconis P, Saloff-coste L. Nash inequality for finite Markov chains. J Theor Prob, 1996, 9(2): 459-510
10. Rosenthal J S. Markov chain convergence: From finite to infinite.'Stoch Proc Appl, 1996, 62(1): 55-72
11. Saloff-Coste L. Convergence to equilibrium and Logarithmic Sobolev constant on manifolds with Ricci curvature bounded below. Coll Math, 1994, 109-121
12. Sinclair A J, Jerrum M R. Approximate counting, uniform generation, and rapidly mixing Markov chains.' Inform and Comput, 1989, 82: 93-133
13. Wang Y Z. Convergehnce rate in total variation for diffusion processes. Preprint 1996