@article{AIHPB_1999__35_4_483_0, author = {Helffer, Bernard}, title = {Remarks on decay of correlations and {Witten} laplacians {III.} {Application} to logarithmic {Sobolev} inequalities}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {483--508}, publisher = {Gauthier-Villars}, volume = {35}, number = {4}, year = {1999}, mrnumber = {1702239}, zbl = {1055.82004}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_1999__35_4_483_0/} }
TY - JOUR AU - Helffer, Bernard TI - Remarks on decay of correlations and Witten laplacians III. Application to logarithmic Sobolev inequalities JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1999 SP - 483 EP - 508 VL - 35 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPB_1999__35_4_483_0/ LA - en ID - AIHPB_1999__35_4_483_0 ER -
%0 Journal Article %A Helffer, Bernard %T Remarks on decay of correlations and Witten laplacians III. Application to logarithmic Sobolev inequalities %J Annales de l'I.H.P. Probabilités et statistiques %D 1999 %P 483-508 %V 35 %N 4 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPB_1999__35_4_483_0/ %G en %F AIHPB_1999__35_4_483_0
Helffer, Bernard. Remarks on decay of correlations and Witten laplacians III. Application to logarithmic Sobolev inequalities. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) no. 4, pp. 483-508. http://archive.numdam.org/item/AIHPB_1999__35_4_483_0/
[1] Weighted spectral gap and logarithmic Sobolev inequalities and their applications, Preprint, 1993. | MR
and ,[2] Decay of correlations and uniqueness of Gibbs lattice systems with nonquadratic interaction, J. Math. Phys. 37 (11) 1996. | MR | Zbl
and ,[3] Diffusions hypercontractives, in: "Séminaire de Probabilités XIX", Lecture Notes in Math., Vol. 1123, Springer, 1985, pp. 179-206. | Numdam | MR | Zbl
and ,[4] Witten Laplacians: Perturbative approach ; Part II Witten Laplacians: Semiclassical approach; Personal communication. | Zbl
, and , Part I[5] Log-Sobolev inequality for unbounded spins systems, Preprint (December 1998), to appear in J. Funct. Anal. (1999). | MR | Zbl
and ,[6] Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators, Commun. Math. Phys. 34 (1973) 251-270. | MR | Zbl
and ,[7] Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models, J. Funct. Anal. 92 (1990) 30-48. | MR | Zbl
and ,[8] Phase transitions, Goldstone bosons and topological superselection rules, Acta Phys. Austriaca, Suppl. XV (1976) 133-269. | MR
,[9] Spectral properties of the Kac operator in large dimension, in: J. Feldman, R. Froese and L.M. Rosen, eds., Proceedings on Mathematical Quantum Theory II: Schrödinger Operators, August 1993; CRM Proceedings and Lecture Notes 8, 1995, pp. 179-211. | MR | Zbl
,[10] Witten Laplacians and Antoniouk's results, Preliminary notes, May 1997.
,[11] Dobrushin's criteria and Antoniouk's results, Preliminary notes, May 1997.
,[12] Remarks on decay of correlations and Witten Laplacians. Brascamp-Lieb inequalities and semi-classical analysis, J. Funct. Anal. 155 (1998) 571-586. | MR | Zbl
,[13] Remarks on decay of correlations and Witten Laplacians. II - Analysis of the dependence on the interaction, Preprint, December 1997; to appear in Rev. in Math. Physics. | MR | Zbl
,[14] On the correlation for Kac like models in the convex case, J. Statist. Phys. 74 (1-2) (1994) 349-369. | MR | Zbl
and ,[15] On the spectral properties of Witten Laplacians, their range projections and Brascamp-Lieb's inequality, Preprint, December 1997.
,[16] Lower bounds for pseudodifferential operators, Ann. Inst. Fourier 40 (1) (1990) 657-682. | Numdam | MR | Zbl
and ,[17] On homogeneization and scaling limit of some gradient perturbations of a massless free field, Commun. Math. Phys. 183 (1997) 55-84. | MR | Zbl
and ,[18] Probability estimates for continuous spin systems, Commun. Math. Phys. 50 (1976) 189-194. | MR
,[19] Essential self-adjointness of Schrödinger operators bounded from below, Math. Z. 159 (1978) 47-50. | MR | Zbl
,[20] Ferromagnetic integrals, correlations and maximum principles, Ann. Inst. Fourier 44 (2) 601-628. | Numdam | MR | Zbl
,[21] Correlation asymptotics and Witten Laplacians (Preprint Ecole Polytechnique, December 1994), St. Petersburg Math. J. 8 (1997) 160-191. | MR | Zbl
,[22] Supersymmetric measures and Maximum principles in the complex domain-Exponential decay of Green's functions, Preprint Ecole Polytechnique, November 1997; to appear in Annales de l'ENS (1999). | Numdam | Zbl
and ,[23] Mean-field bounds and correlation inequalities, J. Statist. Phys. 28 (3) (1982) 431-439. | MR
,[24] The logarithmic Sobolev inequality for continuous spin systems on a lattice, J. Funct. Anal. 104 (1992) 299-326. | MR | Zbl
and ,[25] The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Commun. Math. Phys. 144 (1992) 303-323. | MR | Zbl
and ,[26] The log-Sobolev inequality for weakly coupled φ4-lattice fields, Preprints, October 1997, June 1998; to appear in Prob. Theory Related Fields. | MR | Zbl
,[27] The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice, Commun. Math. Phys. 175 (1996) 401-432. | MR | Zbl
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