Remarks on decay of correlations and Witten laplacians III. Application to logarithmic Sobolev inequalities

 Access to full text

 Full (PDF)

1. [1] A. Val. Antoniouk and A. Vict. Antoniouk, Weighted spectral gap and logarithmic Sobolev inequalities and their applications, Preprint, 1993. MR1265568
2. [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. Zbl0859.60099MR1417151
3. [3] D. Bakry and M. Emery, Diffusions hypercontractives, in: "Séminaire de Probabilités XIX", Lecture Notes in Math., Vol. 1123, Springer, 1985, pp. 179-206. Zbl0561.60080MR889476
4. [4] V. Bach, T. Jecko and J. Sjöstrand, Part I Witten Laplacians: Perturbative approach ; Part II Witten Laplacians: Semiclassical approach; Personal communication. Zbl0877.35084
5. [5] T. Bodineau and B. Helffer, Log-Sobolev inequality for unbounded spins systems, Preprint (December 1998), to appear in J. Funct. Anal. (1999). Zbl0972.82035MR1704666
6. [6] J.M. Combes and L. Thomas, Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators, Commun. Math. Phys.34 (1973) 251-270. Zbl0271.35062MR391792
7. [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. Zbl0705.60066MR1064685
8. [8] J. Fröhlich, Phase transitions, Goldstone bosons and topological superselection rules, Acta Phys. Austriaca, Suppl.XV (1976) 133-269. MR523547
9. [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 Notes8, 1995, pp. 179-211. Zbl0826.35085MR1332041
10. [10] B. Helffer, Witten Laplacians and Antoniouk's results, Preliminary notes, May 1997. 
11. [11] B. Helffer, Dobrushin's criteria and Antoniouk's results, Preliminary notes, May 1997. 
12. [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. Zbl0921.35141MR1624506
13. [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. Zbl1054.82002MR1688446
14. [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. Zbl0946.35508MR1257821
15. [15] J. Johnsen, On the spectral properties of Witten Laplacians, their range projections and Brascamp-Lieb's inequality, Preprint, December 1997. Zbl1023.58012
16. [16] N. Lerner and J. Nourrigat, Lower bounds for pseudodifferential operators, Ann. Inst. Fourier40 (1) (1990) 657-682. Zbl0703.35182MR1091836
17. [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. Zbl0871.35010MR1461951
18. [18] D. Ruelle, Probability estimates for continuous spin systems, Commun. Math. Phys.50 (1976) 189-194. MR424129
19. [19] C.G. Simader, Essential self-adjointness of Schrödinger operators bounded from below, Math. Z.159 (1978) 47-50. Zbl0409.35026MR470456
20. [20] J. Sjöstrand, Ferromagnetic integrals, correlations and maximum principles, Ann. Inst. Fourier44 (2) 601-628. Zbl0831.35031MR1296745
21. [21] J. Sjöstrand, Correlation asymptotics and Witten Laplacians (Preprint Ecole Polytechnique, December 1994), St. Petersburg Math. J.8 (1997) 160-191. Zbl0877.35084MR1392018
22. [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). Zbl0941.47033
23. [23] A.D. Sokal, Mean-field bounds and correlation inequalities, J. Statist. Phys.28 (3) (1982) 431-439. MR668133
24. [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. Zbl0794.46025MR1153990
25. [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. Zbl0745.60104MR1152374
26. [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. Zbl0948.60095MR1715549
27. [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. Zbl0844.46050MR1370101

1. Nobuo Yoshida, The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
2. J. Nourrigat, Exponential of a hamiltonian in large subsets of a lattice and applications
3. Johannes Sjöstrand, Complete asymptotics for correlations of Laplace integrals in the semi-classical limit
4. Michel Ledoux, Logarithmic Sobolev inequalities for unbounded spin systems revisited