Logarithmic Sobolev inequalities for unbounded spin systems revisited
Séminaire de probabilités de Strasbourg, Volume 35  (2001), p. 167-194
@article{SPS_2001__35__167_0,
     author = {Ledoux, Michel},
     title = {Logarithmic Sobolev inequalities for unbounded spin systems revisited},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {35},
     year = {2001},
     pages = {167-194},
     zbl = {0979.60096},
     mrnumber = {1837286},
     language = {en},
     url = {http://www.numdam.org/item/SPS_2001__35__167_0}
}
Ledoux, Michel. Logarithmic Sobolev inequalities for unbounded spin systems revisited. Séminaire de probabilités de Strasbourg, Volume 35 (2001) , pp. 167-194. http://www.numdam.org/item/SPS_2001__35__167_0/

[Ai] S. Aida. Uniform positivity improving property, Sobolev inequalities and spectral gaps. J. Funct. Anal. 158, 152-185 (1998). | MR 1641566 | Zbl 0914.47041

[A-M-S] S. Aida, T. Masuda, I. Shigekawa. Logarithmic Sobolev inequalities and exponential integrability. J. Funct. Anal. 126, 83-101 (1994). | MR 1305064 | Zbl 0846.46020

[An] C. Ané ET AL. Sur les inégalités de Sobolev logarithmiques (2000). Panoramas et Synthèses, S.M.F., to appear. | MR 1845806 | Zbl 0982.46026

[Ba1] D. Bakry. L'hypercontractivité et son utilisation en théorie des semigroupes. Ecole d'Eté de Probabilités de St-Flour. Lecture Notes in Math. 1581, 1-114 (1994). Springer-Verlag. | MR 1307413 | Zbl 0856.47026

[Ba2] D. Bakry. On Sobolev and logarithmic Sobolev inequalities for Markov semigroups. New trends in.Stochastic Analysis. 43-75 (1997). World Scientific. | MR 1654503

[Ba-E] D. Bakry, M. Emery. Diffusions hypercontractives. Séminaire de Probabilités XIX. Lecture Notes in Math. 1123, 177-206 (1985). Springer-Verlag. | Numdam | MR 889476 | Zbl 0561.60080

[Ba-L] D. Bakry, M. Ledoux. Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator. Invent. math. 123, 259-281 (1996). | MR 1374200 | Zbl 0855.58011

[Bo1] S. Bobkov. An isoperimetric inequality on the discrete cube and an elementary proof of the isoperimetric inequality in Gauss space. Ann. Probability 25, 206-214 (1997). | MR 1428506 | Zbl 0883.60031

[Bo2] S. Bobkov. Isoperimetric and analytic inequalities for log-concave probability measures. Ann. Probability 27, 1903-1921 (1999). | MR 1742893 | Zbl 0964.60013

[B-G] S. Bobkov, F. Götze. Exponential integrability and transportation cost related to logarithmic Sobolev inequalities (1998). J. Funct. Anal. 163, 1-28 (1999). | MR 1682772 | Zbl 0924.46027

[B-H1] Th. Bodineau, B. Helffer. On Log-Sobolev inequalities for unbounded spin systems. J. Funct. Anal. 166, 168-178 (1999). | MR 1704666 | Zbl 0972.82035

[B-H2] Th. Bodineau, B. Helffer. Correlations, spectral gaps and Log-Sobolev inequalities for unbounded spins systems. Differential Equations and Mathematical Physics. Birmingham 1999, 27-42. International Press (1999). | MR 1764741 | Zbl 01780486

[B-L] H.J. Brascamp, E.H. Lieb. On extensions of the Brunn-Minkovski and Prékopa-Leindler theorems, including inequalities for log-concave functions, and with an application to the diffusion equation. J. Funct. Anal. 22, 366-389 (1976). | MR 450480 | Zbl 0334.26009

[Fo] P. Fougères. Hypercontractivité et isopérimétrie gaussienne. Applications aux systèmes de spins (1999). Ann. Inst. H. Poincaré, to appear. | Numdam | MR 1792659 | Zbl 0983.60097

[G-H-L] S. Gallot, D. Hulin, J. Lafontaine. Riemannian Geometry. Second Edition. Springer (1990). | MR 1083149 | Zbl 0716.53001

[G-R] I. Gentil, C. Roberto. Spectral gaps for spin system: some non-convex phase examples (2000). J. Funct. Anal., to appear. | MR 1814423 | Zbl 0992.60091

[Gr] L. Gross. Logarithmic Sobolev inequalities. Amer. J. Math. 97, 1061-1083 (1975). | MR 420249 | Zbl 0318.46049

[G-Z] A. Guionnet, B. Zegarlinski. Lectures on logarithmic Sobolev inequalities (2000).

[He1] B. Helffer. Remarks on decay of correlations and Witten Laplacians - Brascamp-Lieb inequalities and semi-classical analysis. J. Funct. Anal. (1999). | MR 1624506 | Zbl 0921.35141

[He2] B. Helffer. Remarks on decay of correlations and Witten Laplacians III- Application to logarithmic Sobolev inequalites. Ann. Inst. H. Poincaré 35, 483-508 (1999). | Numdam | MR 1702239 | Zbl 01340477

[He3] B. Helffer. Semiclassical analysis and statistical mechanics. Notes (1999).

[He-S] B. Helffer, J. Sjöstrand. On the correlation for the Kac like models in the convex case. J. Statist. Phys. 74, 349-369 (1994). | MR 1257821 | Zbl 0946.35508

[H-S] R. Holley, D. Stroock. Logarithmic Sobolev inequalities and stochastic Ising models. J. Statist. Phys. 46, 1159-1194 (1987). | MR 893137 | Zbl 0682.60109

[Le1] M. Ledoux. Concentration of measure and logarithmic Sobolev inequalities. Séminaire de Probabilités XXXIII. Lecture Notes in Math. 1709, 120-216 (1999). Springer. | Numdam | MR 1767995 | Zbl 0957.60016

[Le2] M. Ledoux. The geometry of Markov diffusion generators (1998). Ann. Fac. Sci. Toulouse, to appear. | Numdam | MR 1813804 | Zbl 0980.60097

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

[M-O1] F. Martinelli, E. Olivieri. Approach to equilibrium of Glauber dynamics in the one phase region I. The attractive case. Comm. Math. Phys. 161, 447-486 (1994). | MR 1269387 | Zbl 0793.60110

[M-O2] F. Martinelli, E. Olivieri. Approach to equilibrium of Glauber dynamics in the one phase region II. The general case. Comm. Math. Phys. 161, 487-514 (1994). | MR 1269388 | Zbl 0793.60111

[Ro] G. Royer. Une initiation aux inégalités de Sobolev logarithmiques. Cours Spécialisés. Soc. Math. de France (1999). | MR 1704288 | Zbl 0927.60006

[S-Z1] D. Stroock, B. Zegarlinski. The logarithmic Sobolev inequality for continuous spin systems on a lattice. J. Funct. Anal. 104, 299-326 (1992). | MR 1153990 | Zbl 0794.46025

[S-Z2] D. Stroock, B. Zegarlinski. The logarithmic Sobolev inequality for discrete spin systems on a lattice. Comm. Math. Phys. 149, 175-193 (1992). | MR 1182416 | Zbl 0758.60070

[S-Z3] D. Stroock, B. Zegarlinski. The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition. Comm. Math. Phys. 144, 303-323 (1992). | MR 1152374 | Zbl 0745.60104

[S-Z4] D. Stroock, B. Zegarlinski. On the ergodic properties of Glauber dynamics. J. Stat. Phys. 81, 1007-1019 (1995). | MR 1361304 | Zbl 01554015

[Wa] F.-Y. Wang. Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Probab. Theor. Relat. Fields 109, 417-424 (1997). | MR 1481127 | Zbl 0887.35012

[Yo1] N. Yoshida. The log-Sobolev inequality for weakly coupled lattice fields. Probab. Theor. Relat. Field 115, 1-40 (1999). | MR 1715549 | Zbl 0948.60095

[Yo2] N. Yoshida. Application of log-Sobolev inequality to the stochastic dynamics of unbounded spin systems on the lattice. J. Funct. Anal. 173, 74-102 (2000). | MR 1760279 | Zbl 1040.82047

[Yo3] N. Yoshida. The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice (1999). Ann. Inst. H. Poincaré, to appear. | Numdam | MR 1819124 | Zbl 0992.60089

[Ze1] B. Zegarlinski. The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice. Comm. Math. Phys. 175, 401-432 (1996). | MR 1370101 | Zbl 0844.46050

[Ze2] B. Zegarlinski. Isoperimetry for Gibbs measures (1999).http://www-sv.cict.fr/lsp/Ledoux/