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Referencias:

• Aida, S., Stroock, D.W., Moment estimates derived from Poincaré and logarithmic Sobolev inequalities (1994) Math. Res. Lett., 1, pp. 75-86
• Albeverio, S., Kondratiev, Y.G., Rockner, M., Tsikalenko, T.V., Uniqueness of Gibbs states for quantum lattice systems (1997) C. R. Acad. Sci. Paris, Ser. I, 324, pp. 1401-1406
• Ané, C., Blachère, S., Chafaï, D., Fougères, P., Gentil, I., Malrieu, F., Roberto, C., Scheffer, G., Sur les inégalités de Sobolev logarithmiques (2000) Panoramas et Synthèses, 10. , Société Mathématique de France, Paris
• Bakry, D., L’hypercontractivitè et son utilisation en théorie des semigroups (1994) Séminaire de Probabilités XIX, pp. 1-144. , Volume 1581 of Lecture Notes in Mathematics (Springer, New York,)
• Bakry, D., Emery, M., Difusions hypercontractives (1985) Seminaire de Probabilites XIX, 1123, pp. 177-206. , Springer Lecture Notes in Mathematics
• Balogh, Z.M., Engulatov, A., Hunziker, L., Maasalo, O.E., Functional inequalities and Hamilton Jacobi equations in geodesic spaces (2012) Potential Anal., 36, pp. 317-337
• Baudoin, F., Bonnefont, M., Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality (2012) J. Funct. Anal., 262, pp. 2646-2676
• Bellisard, J., Hoegn-Krohn, R., Compactness and the maximal Gibbs state for random fields on the lattice (1982) Commun. Math. Phys., 84, pp. 297-327
• Bellissard, J., Picco, P., (1978) Lattice quantum fields: Uniqueness and Markov Property, , preprint 78/P. 1059
• Bobkov, S.G., Gotze, F., Exponential integrability and transportation cost related to logarithmic Sobolev inequalities (1999) J. Funct. Anal., 163, pp. 1-28
• Bobkov, S.G., Ledoux, M., From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities (2000) Geom. Funct. Anal., 10, pp. 1028-1052
• Bobkov, S.G., Zegarlinski, B., Entropy bounds and isoperimetry (2005) Mem. Am. Math. Soc., 176, pp. 1-69
• Bodineau, T., Helffer, B., Log-Sobolev inequality for unbounded spin systems (1999) J. Funct. Anal., 166, pp. 168-178
• Bonfiglioni, A., Lanconelli, E., Uguzzoni, F., (2007) Stratified Lie Groups and Potential Theory for Their Sub-Laplacians, , Springer Monographs in Mathematics (Springer, New York,)
• Deuschel, J.D., Stroock, D., (1989) Large Deviations, , Academic Press, San Diego
• Dobrushin, R.L., The problem of uniqueness of a Gibbs random field and the problem of phase transition (1968) Funct. Anal. Appl., 2, pp. 302-312
• Dobrushin, R.L., Prescribing a system of random variables by conditional distributions (1970) Theory Probab. Appl., 15 (3), pp. 458-486
• Dobrushin, R.L., Shlosman, S.B., Completely analytical interactions: Constructive description (1987) J. Stat. Phys., 46, pp. 983-1014
• Dragoni, F., Kontis, V., Zegarlinski, B., Ergodicity of Markov semigroups with Hormander type generators in infinite dimensions (2012) Potential Anal., 37, pp. 199-227
• Gentil, I., Roberto, C., Spectral gaps for spin systems: Some non-convex phase examples (2001) J. Funct. Anal., 180, pp. 66-84
• Georgii, H.O., (1988) Gibbs Measures and Phase Transitions, , Studies in Mathematics 9 (de Gruyter, Berlin, New York,)
• Gross, L., Logarithmic Sobolev inequalities (1976) Am. J. Math., 97, pp. 1061-1083
• Guionnet, A., Zegarlinski, B., (2003) Lectures on Logarithmic Sobolev Inequalities, IHP Course 98, Seminare de Probabilite XXVI, pp. 1-134. , Lecture Notes in Mathematics 1801 (Springer,)
• Hebisch, W., Zegarlinski, B., Coercive inequalities on metric measure spaces (2010) J. Funct. Anal., 258, pp. 814-851
• Helffer, B., (2002) Semiclassical Analysis, Witten Laplacians and Statistical Mechanics, , Partial Differential Equations and Applications (World Scientific, Singapore,)
• Inglis, J., Kontis, V., Zegarlinski, B., From U-bounds to isoperimetry with applications to H-type groups (2011) J. Funct. Anal., 260, pp. 76-116
• Inglis, J., Papageorgiou, I., Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group (2009) Potential Anal., 31, pp. 79-102
• Kontis, V., Ottobre, M., Zegarlinski, B., Markov semigroups with hypocoercive-type generator in infinite dimensions: Ergodicity and smoothing (2016) J. Funct. Anal., 270, pp. 3173-3223
• Lebowitz, J.L., Presutti, E., Statistical mechanics of systems of unbounded spins (1976) Commun. Math. Phys., 50, pp. 195-218
• Ledoux, M., Logarithmic Sobolev inequalities for unbounded spin systems revisited (2001) Seminaire de Probabilites XXXV, pp. 1167-1194. , Lecture Notes in Mathematics 1755 (Springer,)
• Lim, H.Y., Park, Y.M., Yoo, H.J., Dirichlet forms, dirichlet operators, and log-Sobolev inequalities for Gibbs measures of classical unbounded spin system (1997) J. Korean Math. Soc., 34, pp. 731-770
• Marton, K., An inequality for relative entropy and logarithmic Sobolev inequalities in Euclidean spaces (2013) J. Funct. Anal., 264, pp. 34-61
• Marton, K., Logarithmic Sobolev inequalities in discreet product spaces: A proof by a transportation cost distance ; Otto, F., Reznikoff, M., A new criterion for the logarithmic Sobolev inequality and two applications (2007) J. Funct. Anal., 243, pp. 121-157
• Papageorgiou, I., The logarithmic Sobolev inequality in infinite dimensions for unbounded spin systems on the lattice with non quadratic interactions (2010) Markov Process. Relat. Fields, 16, pp. 447-484
• Papageorgiou, I., A note on the modified log-Sobolev inequality (2011) Potential Anal., 35, pp. 275-286
• Papageorgiou, I., The logarithmic Sobolev inequality for Gibbs measures on infinite product of Heisenberg groups (2014) Markov Process. Relat. Fields, 20, pp. 705-749
• Preston, C.J., (1976) Random Fields, , Lecture Notes in Mathematics 534 (Springer,)
• Roberto, C., Zegarlinski, B., Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups (2007) J. Funct. Anal., 243 (1), pp. 28-66
• Rothaus, O., Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities (1985) J. Funct. Anal., 64, pp. 296-313
• Saloff-Coste, L., (2002) Aspects of Sobolev-Type Inequalities, , London Mathematical Society Lecture Note Series 289 (Cambridge University Press, Cambridge,)
• Stroock, D.W., Zegarlinski, B., The equivalence of the logarithmic Sobolev inequalities and the Dobrushin Shlosman mixing condition (1992) Commun. Math. Phys., 144, pp. 303-323
• Varopoulos, N.Th., Saloff-Coste, L., Coulhon, T., Analysis and geometry on groups (1992) Tracts in Mathematics, 100. , Cambridge University Press, Cambridge
• Yoshida, N., The log-Sobolev inequality for weakly coupled lattice field (1999) Probab. Theory Relat. Fields, 115, pp. 1-40
• Yoshida, N., The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice (2001) Ann. Inst. H. Poincaré, Probabilités et Statistiques, 37 (2), pp. 223-243
• Zegarlinski, B., On log-Sobolev inequalities for infinite lattice systems (1990) Lett. Math. Phys., 20, pp. 173-182
• Zegarlinski, B., The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice (1996) Commun. Math. Phys., 175, pp. 401-432
• Zitt, P.A., Functional inequalities and uniqueness of the Gibbs measure - From log-Sobolev to Poincaré (2008) ESAIM Probab. Stat., 12, pp. 258-272

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