A new criterion for the logarithmic Sobolev inequality and two applications

Journal of Functional Analysis

Volumn 243, Issue 1, 2007, Pages 121-157

  Otto, Felix ^a   Reznikoff, Maria G ^b  

^a UNIVERSITY OF BONN   (Germany)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Decay of correlations; Glauber dynamics; Logarithmic Sobolev inequality

Indexed keywords

EID: 33846130924     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.10.002     Document Type: Article

References (21)

1. Bakry D., and Emery M. Diffusions hypercontractives. Séminaire de Probabilités, XIX, Lecture Notes in Math. vol. 1123 (1985), Springer-Verlag 177-206
2. Blower G., and Bolley F. Concentration inequalities on product spaces with applications to Markov processes. math.PR/0505536
3. Bodineau T., and Hellfer B. The log-Sobolev inequality for unbounded spin systems. J. Funct. Anal. 166 (1999) 168-178
4. Gross L. Logarithmic Sobolev inequalities. Amer. J. Math. 97 (1975) 1061-1083
5. N. Grunewald, F. Otto, M.G. Reznikoff, C. Villani, A two-scale proof of a logarithmic Sobolev inequality, SFB preprint, 2005
6. Guionnet A., and Zegarlinski B. Lectures on logarithmic Sobolev inequalities. Séminaire de Probabilités, XXXVI, Lecture Notes in Math. vol. 1801 (2003), Springer-Verlag 1-134
7. Holley R., and Stroock D. Logarithmic Sobolev inequalities and stochastic Ising models. J. Statist. Phys. 46 (1987) 1159-1194
8. Ledoux M. Logarithmic Sobolev inequalities for unbounded spin systems revisited. Séminaire de Probabilités, XXXV, Lecture Notes in Math. vol. 1755 (2001), Springer-Verlag 167-194
9. Lu S.L., and Yau H.T. Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Comm. Math. Phys. 156 (1993) 399-433
10. Martinelli F., and Olivieri E. Approach to equilibrium of Glauber dynamics in the one-phase region. I. The attractive case. Comm. Math. Phys. 161 (1994) 447-486
11. Martinelli F., and Olivieri E. Approach to equilibrium of Glauber dynamics in the one-phase region. II. The general case. Comm. Math. Phys. 161 (1994) 487-514
12. Otto F. The geometry of dissipative evolution equations: The porous medium equation. Comm. Partial Differential Equations 26 (2001) 101-174
13. Otto F., and Villani C. Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173 (2000) 361-400
14. Royer G. Une initiation aux inégalités de Sobolev logarithmiques (1999), Cours Spécialisés, Soc. Math. de France
15. Stroock D.W., and Zegarlinski B. The logarithmic Sobolev inequality for continuous spin systems on a lattice. J. Funct. Anal. 104 (1992) 299-326
16. Stroock D.W., and Zegarlinski B. The logarithmic Sobolev inequality for discrete spin systems on a lattice. Comm. Math. Phys. 149 (1992) 175-193
17. Yoshida N. The log-Sobolev inequality for weakly coupled lattice fields. Probab. Theory Related Fields 115 (1999) 1-40
18. Yoshida N. The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice. Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 223-243
19. Zegarlinski B. Log-Sobolev inequalities for infinite one-dimensional lattice systems. Comm. Math. Phys. 133 (1990) 147-162
20. Zegarlinski B. On log-Sobolev inequalities for infinite lattice systems. Lett. Math. Phys. 20 (1990) 173-182
21. Zegarlinski B. The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice. Comm. Math. Phys. 175 (1996) 401-432