@article{AIHPB_2001__37_2_223_0, author = {Yoshida, Nobuo}, title = {The equivalence of the {log-Sobolev} inequality and a mixing condition for unbounded spin systems on the lattice}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {223--243}, publisher = {Elsevier}, volume = {37}, number = {2}, year = {2001}, mrnumber = {1819124}, zbl = {0992.60089}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_2001__37_2_223_0/} }
TY - JOUR AU - Yoshida, Nobuo TI - The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2001 SP - 223 EP - 243 VL - 37 IS - 2 PB - Elsevier UR - http://archive.numdam.org/item/AIHPB_2001__37_2_223_0/ LA - en ID - AIHPB_2001__37_2_223_0 ER -
%0 Journal Article %A Yoshida, Nobuo %T The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice %J Annales de l'I.H.P. Probabilités et statistiques %D 2001 %P 223-243 %V 37 %N 2 %I Elsevier %U http://archive.numdam.org/item/AIHPB_2001__37_2_223_0/ %G en %F AIHPB_2001__37_2_223_0
Yoshida, Nobuo. The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 223-243. http://archive.numdam.org/item/AIHPB_2001__37_2_223_0/
[1] Logarithmic Sobolev inequalities and exponential integrability, J. Funct. Anal. 126 (1) (1994) 83-101. | MR | Zbl
, , ,[2] Dirichlet operators via stochastic analysis, J. Funct. Anal. 128 (1995) 102-138. | MR | Zbl
, , ,[3] Uniqueness of Gibbs states for quantum lattice systems, Probab. Theory Related Fields 108 (1997) 193-218. | MR | Zbl
, , , ,[4] Diffusions hypercontractives, in: Séminaire de Probabilités XIX, Springer Lecture Notes in Math., 1123, 1985, pp. 177-206. | Numdam | MR | Zbl
, ,[5] Compactness and maximal Gibbs state for random Gibbs fields on the lattice, Comm. Math. Phys. 84 (1982) 297-327. | MR | Zbl
, ,[6] Log-Sobolev inequality for unbounded spin systems, J. Funct. Anal. 166 (1999) 168-178. | MR | Zbl
, ,[7] Correlations, spectral gap and log-Sobolev inequality for unbounded spin systems, in: Differential Equations and Mathematical Physics, Birmingham, International Press, 1999, pp. 27-42. | MR | Zbl
, ,[8] Processus de diffusion associe aux mesures de Gibbs, Z. Wahrsch. verw. Gebiete 46 (1978) 107-124. | MR | Zbl
, ,[9] Constructive criterion for the uniqueness of Gibbs field, in: , , (Eds.), Statistical Physics and Dynamical Systems, Birkhäuser, 1985. | MR | Zbl
, ,[10] Completely analytical Gibbs fields, in: , , (Eds.), Statistical Physics and Dynamical Systems, Birkhäuser, 1985. | MR | Zbl
, ,[11] Completely analytical interactions: Constructive description, J. Stat. Phys. 46 (1987) 983-1014. | MR | Zbl
, ,[12] Large Deviations, Academic Press, 1989. | MR | Zbl
, ,[13] Spectral gaps for spin systems: some non-convex phase examples, preprint, 2000. | MR
, ,[14] Remarks on the decay of correlations and Witten Laplacians III - Application to logarithmic Sobolev inequalities, Ann. de l'Insti. H. Poincaré (Sect. Probab-Stat) (1998). | Numdam | Zbl
,[15] Logarithmic Sobolev inequality and stochastic Ising models, J. Stat. Phys. 46 (1987) 1159-1194. | MR | Zbl
, ,[16] Log-Sobolev inequality for unbounded spin systems revisited, preprint, 1999. | MR
,[17] Interacting Particle Systems, Springer Verlag, Berlin, 1985. | MR | Zbl
,[18] Lectures on the Coupling Method, Wiley, 1992. | MR | Zbl
,[19] Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 399-433. | MR | Zbl
, ,[20] Approach to equilibrium of Glauber dynamics in the one phase region I: Attractive case, Comm. Math. Phys. 161 (1994) 447-486. | MR | Zbl
, ,[21] Approach to equilibrium of Glauber dynamics in the one phase region II: General case, Comm. Math. Phys. 161 (1994) 487-514. | MR | Zbl
, ,[22] Multidimensional Diffusion Processes, Springer Verlag, Berlin, 1979. | MR | Zbl
, ,[23] The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Comm. Math. Phys. 144 (1992) 303-323. | MR | Zbl
, ,[24] The logarithmic Sobolev inequality for discrete spin systems on the lattice, Comm. Math. Phys. 149 (1992) 175-193. | MR | Zbl
, ,[25] Sugiura M., Private communication.
[26] Sobolev spaces on a Riemannian manifold and their equivalence, J. Math. Kyoto Univ. 33 (1992) 621-654. | MR | Zbl
,[27] The log-Sobolev inequality for weakly coupled lattice fields, Probab. Theory Related Fields 115 (1999) 1-40. | MR | Zbl
,[28] Application of log-Sobolev inequality to the stochastic dynamics of unbounded spin systems on the lattice, J. Funct. Anal. 173 (2000) 74-102. | MR | Zbl
,[29] The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice, Comm. Math. Phys. 175 (1996) 401-432. | MR | Zbl
,