@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}, pages = {167--194}, publisher = {Springer - Lecture Notes in Mathematics}, volume = {35}, year = {2001}, mrnumber = {1837286}, zbl = {0979.60096}, language = {en}, url = {http://www.numdam.org/item/SPS_2001__35__167_0/} }
TY - JOUR AU - Ledoux, Michel TI - Logarithmic Sobolev inequalities for unbounded spin systems revisited JO - Séminaire de probabilités de Strasbourg PY - 2001 SP - 167 EP - 194 VL - 35 PB - Springer - Lecture Notes in Mathematics UR - http://www.numdam.org/item/SPS_2001__35__167_0/ LA - en ID - SPS_2001__35__167_0 ER -
%0 Journal Article %A Ledoux, Michel %T Logarithmic Sobolev inequalities for unbounded spin systems revisited %J Séminaire de probabilités de Strasbourg %D 2001 %P 167-194 %V 35 %I Springer - Lecture Notes in Mathematics %U http://www.numdam.org/item/SPS_2001__35__167_0/ %G en %F 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] Uniform positivity improving property, Sobolev inequalities and spectral gaps. J. Funct. Anal. 158, 152-185 (1998). | MR | Zbl
.[A-M-S] Logarithmic Sobolev inequalities and exponential integrability. J. Funct. Anal. 126, 83-101 (1994). | MR | Zbl
, , .[An] Sur les inégalités de Sobolev logarithmiques (2000). Panoramas et Synthèses, S.M.F., to appear. | MR | Zbl
ET AL.[Ba1] 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 | Zbl
.[Ba2] On Sobolev and logarithmic Sobolev inequalities for Markov semigroups. New trends in.Stochastic Analysis. 43-75 (1997). World Scientific. | MR
.[Ba-E] Diffusions hypercontractives. Séminaire de Probabilités XIX. Lecture Notes in Math. 1123, 177-206 (1985). Springer-Verlag. | Numdam | MR | Zbl
, .[Ba-L] Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator. Invent. math. 123, 259-281 (1996). | MR | Zbl
, .[Bo1] 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 | Zbl
.[Bo2] Isoperimetric and analytic inequalities for log-concave probability measures. Ann. Probability 27, 1903-1921 (1999). | MR | Zbl
.[B-G] Exponential integrability and transportation cost related to logarithmic Sobolev inequalities (1998). J. Funct. Anal. 163, 1-28 (1999). | MR | Zbl
, .[B-H1] On Log-Sobolev inequalities for unbounded spin systems. J. Funct. Anal. 166, 168-178 (1999). | MR | Zbl
, .[B-H2] Correlations, spectral gaps and Log-Sobolev inequalities for unbounded spins systems. Differential Equations and Mathematical Physics. Birmingham 1999, 27-42. International Press (1999). | MR | Zbl
, .[B-L] 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 | Zbl
, .[Fo] Hypercontractivité et isopérimétrie gaussienne. Applications aux systèmes de spins (1999). Ann. Inst. H. Poincaré, to appear. | Numdam | MR | Zbl
.[G-H-L] Riemannian Geometry. Second Edition. Springer (1990). | MR | Zbl
, , .[G-R] Spectral gaps for spin system: some non-convex phase examples (2000). J. Funct. Anal., to appear. | MR | Zbl
, .[Gr] Logarithmic Sobolev inequalities. Amer. J. Math. 97, 1061-1083 (1975). | MR | Zbl
.[G-Z] Lectures on logarithmic Sobolev inequalities (2000).
, .[He1] Remarks on decay of correlations and Witten Laplacians - Brascamp-Lieb inequalities and semi-classical analysis. J. Funct. Anal. (1999). | MR | Zbl
.[He2] Remarks on decay of correlations and Witten Laplacians III- Application to logarithmic Sobolev inequalites. Ann. Inst. H. Poincaré 35, 483-508 (1999). | Numdam | MR | Zbl
.[He3] Semiclassical analysis and statistical mechanics. Notes (1999).
.[He-S] On the correlation for the Kac like models in the convex case. J. Statist. Phys. 74, 349-369 (1994). | MR | Zbl
, .[H-S] Logarithmic Sobolev inequalities and stochastic Ising models. J. Statist. Phys. 46, 1159-1194 (1987). | MR | Zbl
, .[Le1] Concentration of measure and logarithmic Sobolev inequalities. Séminaire de Probabilités XXXIII. Lecture Notes in Math. 1709, 120-216 (1999). Springer. | Numdam | MR | Zbl
.[Le2] The geometry of Markov diffusion generators (1998). Ann. Fac. Sci. Toulouse, to appear. | Numdam | MR | Zbl
.[L-Y] Spectral gap and logarithmic Sobolev inequalities for Kawasaki and Glauber dynamics. Comm. Math. Phys. 156, 399-433 (1993). | MR | Zbl
, .[M-O1] Approach to equilibrium of Glauber dynamics in the one phase region I. The attractive case. Comm. Math. Phys. 161, 447-486 (1994). | MR | Zbl
, .[M-O2] Approach to equilibrium of Glauber dynamics in the one phase region II. The general case. Comm. Math. Phys. 161, 487-514 (1994). | MR | Zbl
, .[Ro] Une initiation aux inégalités de Sobolev logarithmiques. Cours Spécialisés. Soc. Math. de France (1999). | MR | Zbl
.[S-Z1] The logarithmic Sobolev inequality for continuous spin systems on a lattice. J. Funct. Anal. 104, 299-326 (1992). | MR | Zbl
, .[S-Z2] The logarithmic Sobolev inequality for discrete spin systems on a lattice. Comm. Math. Phys. 149, 175-193 (1992). | MR | Zbl
, .[S-Z3] The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition. Comm. Math. Phys. 144, 303-323 (1992). | MR | Zbl
, .[S-Z4] On the ergodic properties of Glauber dynamics. J. Stat. Phys. 81, 1007-1019 (1995). | MR | Zbl
, .[Wa] Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Probab. Theor. Relat. Fields 109, 417-424 (1997). | MR | Zbl
.[Yo1] The log-Sobolev inequality for weakly coupled lattice fields. Probab. Theor. Relat. Field 115, 1-40 (1999). | MR | Zbl
.[Yo2] Application of log-Sobolev inequality to the stochastic dynamics of unbounded spin systems on the lattice. J. Funct. Anal. 173, 74-102 (2000). | MR | Zbl
.[Yo3] 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 | Zbl
.[Ze1] The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice. Comm. Math. Phys. 175, 401-432 (1996). | MR | Zbl
.[Ze2] Isoperimetry for Gibbs measures (1999).http://www-sv.cict.fr/lsp/Ledoux/
.