Hypercontractivité et isopérimétrie gaussienne. Applications aux systèmes de spins
Annales de l'I.H.P. Probabilités et statistiques (2000)
- Volume: 36, Issue: 5, page 647-689
- ISSN: 0246-0203
Access Full Article
topHow to cite
topReferences
top- [1] Bakry D., L'hypercontractivité et son utilisation en théorie des semi-groupes, Ecole d'été de Probabilités de Saint Flour1992, Lecture Notes in Math., Vol. 1581, Springer, 1994. Zbl0856.47026MR1307413
- [2] Bakry D., On Sobolev and logarithmic Sobolev inequalities for Markov semigroups, in: Proceedings of the Taniguchi Symposium, Warwick, 1994.
- [3] Bakry D., Emery M., Hypercontractivité des semi-groupes de diffusion, C. R. Acad. Sc. Paris, Série I 299 (15) (1984). Zbl0563.60068MR772092
- [4] Bakry D., Ledoux M., Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator, Invent. Math.123 (2) (1996) 259-281. Zbl0855.58011MR1374200
- [5] Bakry D., Michel D., Sur les inégalités FKG, Annales de la Faculté des Sciences de ToulouseXI (2) (1990).
- [6] Barthe F., Maurey B., Some remarks on isoperimetry of Gaussian type, Preprint, 1999. Zbl0964.60018
- [7] Bobkov S., A functional form of the isoperimetric inequality for the Gaussian measure, J. Functional Analysis135 (1996) 39-49. Zbl0838.60013MR1367623
- [8] Bobkov S., An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space, Ann. Probab.25 (1997) 206-214. Zbl0883.60031MR1428506
- [9] Carlen E.A., Stroock D.W., An application of the Bakry-Emery criterion to infinite dimensional diffusions, Séminaire de Probabilités, Lecture Notes in Math., Vol. 1204, Springer, Berlin, 1986. Zbl0609.60086MR942029
- [10] Diaconis P., Saloff-Coste L., Logarithmic Sobolev inequalities for finite Markov chains, Ann. Appl. Probab.6 (3) (1996) 695-750. Zbl0867.60043MR1410112
- [11] Ellis R., Entropy, Large Deviations and Statistical Mechanics, Grundlehren der Mathematischen Wissenschaften, Vol. 271, Springer, 1985. Zbl0566.60097MR793553
- [12] Georgii H.-O., Gibbs Measures and Phase Transitions, De Gruyter, Berlin, 1988. Zbl0657.60122MR956646
- [13] Holley R., Stroock D.W., Logarithmic Sobolev inequalities and stochastic Ising models, J. Statist. Phys.46 (4-5) (1987). Zbl0682.60109MR893137
- [14] Holley R., Stroock D.W., Uniform and L2 convergence in one dimensional stochastic Ising models, Comm. Math. Phys.123 (1989) 85-93. Zbl0666.60104MR1002033
- [15] Laroche E., Hypercontractivité pour des systèmes de spins de portée infinie, Probab. Theory Related Fields101 (1995) 89-132. Zbl0820.60082MR1314176
- [16] Ledoux M., On Talagrand's deviation inequalities for product measures, ESAIM Probab. Statist. 1 (1995/97) 63-87. Zbl0869.60013MR1399224
- [17] Ledoux M., Isoperimetry and Gaussian analysis, in: Lectures on Probability Theory and Statistics (Saint-Flour, 1994), Lecture Notes in Math., Vol. 1648, Springer, Berlin, 1996, pp. 165-294. Zbl0874.60005MR1600888
- [18] Ledoux M., Concentration of measure and logarithmic Sobolev inequalities, Preprint (To appear in: Séminaire de Probabilités, Lecture Notes in Math., Springer). Zbl0957.60016MR1767995
- [19] Stroock D.W., Zegarlinski B., The logarithmic Sobolev inequality for continuous spin systems on a lattice, J. Functional Anal.104 (1992) 299-326. Zbl0794.46025MR1153990
- [20] Stroock D.W., Zegarlinski B., The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Comm. Math. Phys.144 (2) (1992) 303-323. Zbl0745.60104MR1152374
- [21] Stroock D.W., Zegarlinski B., On the ergodic properties of Glauber dynamics, J. Statist. Phys.81 (5/6) (1995). Zbl1081.60562MR1361304
- [22] Yoshida N., The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice, Preprint, 1998.
- [23] Zegarlinski B., Log-Sobolev inequalities for infinite one-dimensional lattice systems, Comm. Math. Phys.133 (1) (1990) 147-162. Zbl0713.60080MR1071239
- [24] Zegarlinski B., Dobrushin uniqueness theorem and logarithmic Sobolev inequalities, J. Functional Anal.105 (1992) 77-111. Zbl0761.46020MR1156671
- [25] Zegarlinski B., Isoperimetry for Gibbs measures, Preprint, 1999. MR1849178