Estimate of spectral gap for continuous gas

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 40, Issue 4, 2004, Pages 387-409

  Wu, Liming ^a,b  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b WUHAN UNIVERSITY   (China)

Author keywords

Birth and death processes; Gibbs measures; Poincar inequality

Indexed keywords

EID: 2942644308     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2003.11.003     Document Type: Article

References (23)

1. Ané C. Ledoux M. On logarithmic Sobolev inequalities for continuous random walks on graphs Probab. Theory Related Fields 116 2000 573-602
2. Bodineau T. Heffler B. The log-Sobolev inequality for unbounded spin systems J. Funct. Anal. 166 1 1999 168-178
3. Bodineau T. Heffler B. Correlation, spectral gap and log-Sobolev inequalities for unbounded spin systems Differential Equations and Math. Phys. 2000 51-66 Amer. Math. Soc. Providence, RI
4. Bertini L. Cancrini N. Cesi F. The spectral gap for a Glauber-type dynamics in a continuous gas Ann. Inst. H. Poincaré PR 38 1 2002 91-108
5. Cesi F. Quasi-factorisation of entropy and log-Sobolev inequalities for Gibbs random fields Probab. Theory Related Fields 120 2001 569-584
6. Dai Pra P. Paganoni A.M. Posta G. Entropy inequalities for unbounded spin systems Ann. Probab. 30 4 2000 1959-1976
7. Holley A. Stroock D.W. Nearest neighbor birth and death processes on the real line Acta Mathematica 140 1978 103-154
8. Kallenberg O. Foundations of Modern Probability 1997 Springer-Verlag
9. Martinelli F. Lectures on Glauber dynamics for discrete spin models Ecole d'Eté de Saint-Flour (1997) Lect. Notes in Math. vol. 1717 1999 93-191 Springer
10. Ledoux M. Logarithmic Sobolev inequalities for unbounded spin systems revisited Séminaire de Probabilités Lect. Notes Math. vol. 1755 2001 167-194 Springer
11. Ligget T.M. Interacting Particle Systems 1985 Springer-Verlag
12. Lu S.L. Yau H.T. Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics Comm. Math. Phys. 156 1993 399-433
13. Yu. Kondratiev, E. Lytvynov, Glauber dynamics of continuous particle systems, Preprint, 2003
14. Mao Y.H. Strong ergodicity for Markov processes by coupling method J. Appl. Probab. 39 4 2002 839-852
15. Olla S. Tremoulet C. Equilibrium fluctuations for interacting Ornstein-Uhlenbeck particles Comm. Math. Phys. 2003
16. Picard J. Formule de dualité sur l'espace de Poisson Ann. Inst. H. Poincaré (Prob. Stat.) 32 4 1996 509-548
17. Ruelle D. Statistical Mechanics: Rigorous Results 1969 Benjamin
18. Stroock D.W. Zegarlinski B. The equivalence between the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition Comm. Math. Phys. 144 1992 303-323
19. Stroock D.W. Zegarlinski B. The logarithmic Sobolev inequality for discrete spin systems on the lattice Comm. Math. Phys. 149 1992 175-193
20. Surgailis D. On the multiple Poisson stochastic integrals and associated Markov semigroups Probab. Math. Stat. 3 1984 217-239
21. Wu L. A new modified logarithmic Sobolev inequality for Poisson point processes and several applications Probab. Theory Related Fields 118 2000 427-438
22. Wu L. Uniqueness of Nelson's diffusions Probab. Theory Related Fields 114 1999 549-585
23. Yoshida N. The equivalence of the logarithmic Sobolev inequality and a mixing condition for unbounded spin systems on the lattice Ann. Inst. H. Poincaré (Prob. Stat.) 37 2001 223-243