The spectral gap for a Glauber-type dynamics in a continuous gas
Bertini, Lorenzo ; Cancrini, Nicoletta ; Cesi, Filippo
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 91-108 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2002__38_1_91_0,
     author = {Bertini, Lorenzo and Cancrini, Nicoletta and Cesi, Filippo},
     title = {The spectral gap for a Glauber-type dynamics in a continuous gas},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {38},
     year = {2002},
     pages = {91-108},
     mrnumber = {1899231},
     zbl = {0994.82054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2002__38_1_91_0}
}

Bertini, Lorenzo; Cancrini, Nicoletta; Cesi, Filippo. The spectral gap for a Glauber-type dynamics in a continuous gas. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) pp. 91-108. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_1_91_0/

[1] F Cesi, C Maes, F Martinelli, Relaxation of disordered magnets in the Griffiths regime, Comm. Math. Phys. 188 (1997) 135-173. | MR 1471335 | Zbl 0882.60095

[2] E.B Davies, Heat Kernels and Spectral Theory, Cambridge Univ. Press, 1989. | MR 990239 | Zbl 0699.35006

[3] R Fernández, P.A Ferrari, N.L Garcia, Perfect simulation for interacting point processes, loss networks and Ising models, Preprint, 1999. | MR 1934155

[4] M Ledoux, Logarithmic Sobolev inequalities for unbounded spin systems revisited, in: Séminaire de Probabilités, XXXV (Berlin), Springer, Berlin, 2001, pp. 167-194. | Numdam | MR 1837286 | Zbl 0979.60096

[5] M Ledoux, Concentration of measure and logarithmic Sobolev inequalities, in: Séminaire de Probabilités, XXXIII, Lecture Notes in Mathematics, 1709, Springer, Berlin, 1999, pp. 120-216. | Numdam | MR 1767995 | Zbl 0957.60016

[6] T.M Liggett, Interacting Particle Systems, Springer, Berlin, 1985. | MR 776231 | Zbl 1103.82016

[7] S.L Lu, H.T Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 399-433. | MR 1233852 | Zbl 0779.60078

[8] F Martinelli, Lectures on Glauber dynamics for discrete spin models, in: Lectures on Probability Theory and Statistics (Saint-Flour, 1997), Lecture Notes in Mathematics, 1717, Springer, Berlin, 1999, pp. 93-191. | MR 1746301 | Zbl 1051.82514

[9] F Martinelli, E Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region I: The attractive case, Comm. Math. Phys. 161 (1994) 447. | MR 1269387 | Zbl 0793.60110

[10] F Martinelli, E Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region II: The general case, Comm. Math. Phys. 161 (1994) 487. | MR 1269388 | Zbl 0793.60111

[11] K Matthes, J Kerstan, J Mecke, Infinitely Divisible Point Processes, Wiley, Chichester, 1978. | MR 517931

[12] C Preston, 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. | MR 474532 | Zbl 0379.60082

[13] D Ruelle, Superstable interactions in classical statistical mechanics, Comm. Math. Phys. 18 (1970) 127-159. | MR 266565 | Zbl 0198.31101

[14] H Spohn, Equilibrium fluctuations for interacting Brownian particles, Comm. Math. Phys. 103 (1986) 1-33. | MR 826856 | Zbl 0605.60092

[15] D.W Stroock, B Zegarlinski, The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Comm. Math. Phys. 144 (1992) 303-323. | Zbl 0745.60104

[16] D.W Stroock, B Zegarlinski, The logarithmic Sobolev inequality for discrete spin on a lattice, Comm. Math. Phys. 149 (1992) 175. | MR 1182416 | Zbl 0758.60070

[17] N Yoshida, 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. | Numdam | MR 1819124 | Zbl 0992.60089

[18] B Zegarlinski, The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice, Comm. Math. Phys. 175 (1996) 401-432. | MR 1370101 | Zbl 0844.46050