The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 4, p. 385-436
@article{AIHPB_2002__38_4_385_0,
     author = {Cancrini, N. and Martinelli, Fabio and Roberto, C.},
     title = {The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {38},
     number = {4},
     year = {2002},
     pages = {385-436},
     zbl = {01783420},
     mrnumber = {1914934},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2002__38_4_385_0}
}
Cancrini, N.; Martinelli, F.; Roberto, C. The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited. Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 4, pp. 385-436. http://www.numdam.org/item/AIHPB_2002__38_4_385_0/

[1] C. Albanese, A Goldstone mode in the Kawasaki-Ising model, J. Stat. Phys. 77 (1/2) (1994) 77-87. | Zbl 0837.60094

[2] C. Ané et al., Sur les inégalités de Sobolev logarithmiques, Panoramas et Synthèses 10 (2001), S.M.F.

[3] Bertini L., Cancrini N., Cesi F., The spectral gap for a Glauber-type dynamics in a continuous gas, Preprint n. 00-249 on http://rene.ma.utexas.edu/mp_ arc.

[4] L. Bertini, E.N.M. Cirillo, E. Olivieri, Renormalization-group transformations under strong mixing conditions: Gibbsianness and convergence of renormalized interactions, J. Stat. Phys. 97 (1999) 831-915. | MR 1734386 | Zbl 0958.82017

[5] L. Bertini, B. Zegarlinski, Coercive inequalities for Gibbs measures, J. Funct. Anal. 162 (1999) 257-289. | MR 1682059 | Zbl 0932.60061

[6] L. Bertini, B. Zegarlinski, Coercive inequalities for Kawasaki dynamics. The product case, Markov Proc. Related Fields 5 (1999) 125-162. | MR 1762171 | Zbl 0934.60096

[7] N. Cancrini, F. Cesi, F. Martinelli, Kawasaki dynamics at low temperature, J. Stat. Phys. 95 (1/2) (1999) 219-275. | MR 1705586 | Zbl 0941.60092

[8] F. Cesi, Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields, Probab. Theory Related Fields (2001), To appear. | MR 1853483 | Zbl 1086.82002

[9] N. Cancrini, F. Martinelli, Comparison of finite volume canonical and grand canonical Gibbs measures under a mixing condition, Markov Proc. Related Fields 6 (2000) 1-49. | MR 1758982 | Zbl 1005.82017

[10] N. Cancrini, F. Martinelli, On the spectral gap of Kawasaki dynamics under a mixing condition revisited, J. Math. Phys. 41 (2000) 1391-1423. | MR 1757965 | Zbl 0977.82031

[11] N. Cancrini, F. Martinelli, Diffusive scaling of the spectral gap for the dilute Ising lattice gas under the percolation threshold, Probab. Theory Related Fields (2001), To appear. | MR 1853481 | Zbl 1086.82018

[12] P. Diaconis, L. Saloff-Coste, Logarithmic Sobolev inequality for finite Markov chains, Ann. Appl. Probab. 6 (3) (1996) 695-750. | MR 1410112 | Zbl 0867.60043

[13] H.O. Georgii, Gibbs Measures and Phase Transitions, De Gruyter Series in Mathematics, 9, Walter de Gruyter, Berlin, 1988. | MR 956646 | Zbl 0657.60122

[14] S.T. 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

[15] T.-Y.T. Lee, H.-T. Yau, Logarithmic Sobolev inequality for some models of random walks, Ann. Probab. 26 (4) (1998) 1855-1873. | MR 1675008 | Zbl 0943.60062

[16] F. Martinelli, Lectures on Glauber dynamics for discrete spin models, Proceedings of the Saint Flour Summer School in Probability Theory, Lecture Notes in Math., 1717, 1997. | MR 1746301 | Zbl 1051.82514

[17] L. Miclo, An example of application of discrete Hardy's inequalities, Markov Process. Related Fields 5 (1999) 319-330. | MR 1710983 | Zbl 0942.60081

[18] S.R.S. Varadhan, H.-T. Yau, Diffusive limit of lattice gas with mixing conditions, Asian J. Math. 1 (4) (1997) 623-678. | MR 1621569 | Zbl 0947.60089

[19] H.-T. Yau, Logarithmic Sobolev inequality for lattice gases with mixing conditions, Comm. Math. Phys. 181 (1996) 367-408. | MR 1414837 | Zbl 0864.60079

[20] H.-T. Yau, Logarithmic Sobolev inequality for generalized simple exclusion processes, Probab. Theory Related Fields 109 (4) (1997) 507-538. | MR 1483598 | Zbl 0903.60087