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.
@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},
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year = {1999},
zbl = {1055.82004},
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language = {en},
url = {http://archive.numdam.org/item/AIHPB_1999__35_4_483_0/}
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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] A. Val. Antoniouk and A. Vict. Antoniouk, Weighted spectral gap and logarithmic Sobolev inequalities and their applications, Preprint, 1993. | MR 1265568

[2] A. Val. Antoniouk and A. Vict. Antoniouk, Decay of correlations and uniqueness of Gibbs lattice systems with nonquadratic interaction, J. Math. Phys. 37 (11) 1996. | MR 1417151 | Zbl 0859.60099

[3] D. Bakry and M. Emery, Diffusions hypercontractives, in: "Séminaire de Probabilités XIX", Lecture Notes in Math., Vol. 1123, Springer, 1985, pp. 179-206. | Numdam | MR 889476 | Zbl 0561.60080

[4] V. Bach, T. Jecko and J. Sjöstrand, Part I Witten Laplacians: Perturbative approach ; Part II Witten Laplacians: Semiclassical approach; Personal communication. | Zbl 0877.35084

[5] T. Bodineau and B. Helffer, Log-Sobolev inequality for unbounded spins systems, Preprint (December 1998), to appear in J. Funct. Anal. (1999). | MR 1704666 | Zbl 0972.82035

[6] J.M. Combes and L. Thomas, Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators, Commun. Math. Phys. 34 (1973) 251-270. | MR 391792 | Zbl 0271.35062

[7] J.-D. Deuschel and D. Strook, Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models, J. Funct. Anal. 92 (1990) 30-48. | MR 1064685 | Zbl 0705.60066

[8] J. Fröhlich, Phase transitions, Goldstone bosons and topological superselection rules, Acta Phys. Austriaca, Suppl. XV (1976) 133-269. | MR 523547

[9] B. Helffer, 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 1332041 | Zbl 0826.35085

[10] B. Helffer, Witten Laplacians and Antoniouk's results, Preliminary notes, May 1997.

[11] B. Helffer, Dobrushin's criteria and Antoniouk's results, Preliminary notes, May 1997.

[12] B. Helffer, Remarks on decay of correlations and Witten Laplacians. Brascamp-Lieb inequalities and semi-classical analysis, J. Funct. Anal. 155 (1998) 571-586. | MR 1624506 | Zbl 0921.35141

[13] B. Helffer, 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 1688446 | Zbl 1054.82002

[14] B. Helffer and J. Sjöstrand, On the correlation for Kac like models in the convex case, J. Statist. Phys. 74 (1-2) (1994) 349-369. | MR 1257821 | Zbl 0946.35508

[15] J. Johnsen, On the spectral properties of Witten Laplacians, their range projections and Brascamp-Lieb's inequality, Preprint, December 1997.

[16] N. Lerner and J. Nourrigat, Lower bounds for pseudodifferential operators, Ann. Inst. Fourier 40 (1) (1990) 657-682. | Numdam | MR 1091836 | Zbl 0703.35182

[17] A. Naddaf and T. Spencer, On homogeneization and scaling limit of some gradient perturbations of a massless free field, Commun. Math. Phys. 183 (1997) 55-84. | MR 1461951 | Zbl 0871.35010

[18] D. Ruelle, Probability estimates for continuous spin systems, Commun. Math. Phys. 50 (1976) 189-194. | MR 424129

[19] C.G. Simader, Essential self-adjointness of Schrödinger operators bounded from below, Math. Z. 159 (1978) 47-50. | MR 470456 | Zbl 0409.35026

[20] J. Sjöstrand, Ferromagnetic integrals, correlations and maximum principles, Ann. Inst. Fourier 44 (2) 601-628. | Numdam | MR 1296745 | Zbl 0831.35031

[21] J. Sjöstrand, Correlation asymptotics and Witten Laplacians (Preprint Ecole Polytechnique, December 1994), St. Petersburg Math. J. 8 (1997) 160-191. | MR 1392018 | Zbl 0877.35084

[22] J. Sjöstrand and W.M. Wang, 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 0941.47033

[23] A.D. Sokal, Mean-field bounds and correlation inequalities, J. Statist. Phys. 28 (3) (1982) 431-439. | MR 668133

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

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

[26] N. Yoshida, The log-Sobolev inequality for weakly coupled φ4-lattice fields, Preprints, October 1997, June 1998; to appear in Prob. Theory Related Fields. | MR 1715549 | Zbl 0948.60095

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