The spectral gap for a Glauber-type dynamics in a continuous gas

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

Volumn 38, Issue 1, 2002, Pages 91-108

  Bertini, Lorenzo ^a   Cancrini, Nicoletta ^b,d   Cesi, Filippo ^c,d  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^d INFM   (Italy)

Author keywords

Birth and death processes; Continuous systems; Gibbs measures; Spectral gap

Indexed keywords

EID: 0344793450     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(01)01085-8     Document Type: Article

References (18)

1. Cesi F., Maes C., Martinelli F., Relaxation of disordered magnets in the Griffiths regime, Comm. Math. Phys. 188 (1997) 135-173.
2. Davies E.B., Heat Kernels and Spectral Theory, Cambridge Univ. Press, 1989.
3. Fernândez R., Ferrari P.A., Garcia N.L., Perfect simulation for interacting point processes, loss networks and Ising models, Preprint, 1999.
4. Ledoux M., Logarithmic Sobolev inequalities for unbounded spin systems revisited, in: Séminaire de Probabilités, XXXV (Berlin), Springer, Berlin, 2001, pp. 167-194.
5. Ledoux M., Concentration of measure and logarithmic Sobolev inequalities, in: Séminaire de Probabilités, XXXIII, Lecture Notes in Mathematics, Vol. 1709, Springer, Berlin, 1999, pp. 120-216.
6. Liggett T.M., Interacting Particle Systems, Springer, Berlin, 1985.
7. Lu S.L., Yau H.T., Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 399-433.
8. Martinelli F., Lectures on Glauber dynamics for discrete spin models, in: Lectures on Probability Theory and Statistics (Saint-Flour, 1997), Lecture Notes in Mathematics, Vol. 1717, Springer, Berlin, 1999, pp. 93-191.
9. Martinelli F., Olivieri E., Approach to equilibrium of Glauber dynamics in the one phase region I: The attractive case, Comm. Math. Phys. 161 (1994) 447.
10. Martinelli F., Olivieri E., Approach to equilibrium of Glauber dynamics in the one phase region II: The general case, Comm. Math. Phys. 161 (1994) 487.
11. Matthes K., Kerstan J., Mecke J., Infinitely Divisible Point Processes, Wiley, Chichester, 1978.
12. Preston C., Spatial birth-and-death processes, Proceedings of the 40th Session of the International Statistical Institute (Warsaw, 1975), Bull. Inst. Internat. Statist. 46 (1975) 371-391.
13. Ruelle D., Superstable interactions in classical statistical mechanics, Comm. Math. Phys. 18 (1970) 127-159.
14. Spohn H., Equilibrium fluctuations for interacting Brownian particles, Comm. Math. Phys. 103 (1986) 1-33.
15. Stroock D.W., Zegarlinski B., The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Comm. Math. Phys. 144 (1992) 303-323.
16. Stroock D.W., Zegarlinski B., The logarithmic Sobolev inequality for discrete spin on a lattice, Comm. Math. Phys. 149 (1992) 175.
17. Yoshida N., The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice, Ann. Inst. H. Poincaré Probab. Statist. 37 (2) (2001) 223-243.
18. Zegarlinski B., The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice, Comm. Math. Phys. 175 (1996) 401-432.