The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Bakry, D.; Émery, Michel. Diffusions hypercontractives. (French) [Hypercontractive diffusions] Séminaire de probabilités, XIX, 1983/84, 177--206, Lecture Notes in Math., 1123, Springer, Berlin, 1985. MR0889476
  • Béllissard, Jean; Høegh-Krohn, Raphael. Compactness and the maximal Gibbs state for random Gibbs fields on a lattice. Comm. Math. Phys. 84 (1982), no. 3, 297--327. MR0667405
  • Bodineau, T.; Helffer, B. The log-Sobolev inequality for unbounded spin systems. J. Funct. Anal. 166 (1999), no. 1, 168--178. MR1704666
  • Dizdar, D. Schritte zu einer optimalen Konvergenzrate im hydrodynamischen Limes der Kawasaki Dynamik (towards an optimal rate of convergence in the hydrodynamic limit for Kawasaki dynamics), Ph.D. thesis, Diploma thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, 2007.
  • Gross, Leonard. Logarithmic Sobolev inequalities. Amer. J. Math. 97 (1975), no. 4, 1061--1083. MR0420249
  • Grunewald, Natalie; Otto, Felix; Villani, Cédric; Westdickenberg, Maria G. A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009), no. 2, 302--351. MR2521405
  • Holley, Richard; Stroock, Daniel. Logarithmic Sobolev inequalities and stochastic Ising models. J. Statist. Phys. 46 (1987), no. 5-6, 1159--1194. MR0893137
  • Horiguchi, T.; Morita, T. Upper and lower bounds to a correlation function for an Ising model with random interactions. Phys. Lett. A 74 (1979), no. 5, 340--342. MR0591328
  • Ledoux, M. Logarithmic Sobolev inequalities for unbounded spin systems revisited. Séminaire de Probabilités, XXXV, 167--194, Lecture Notes in Math., 1755, Springer, Berlin, 2001. MR1837286
  • Martinelli, F.; Olivieri, E. Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case. Comm. Math. Phys. 161 (1994), no. 3, 447--486. MR1269387
  • Menz, Georg; A Brascamp-Lieb type covariance estimate, Electron. J. Probab. 19 (2014), no. 78, 1--15.
  • Menz, Georg; Nittka, Robin. Decay of correlations in 1D lattice systems of continuous spins and long-range interaction. J. Stat. Phys. 156 (2014), no. 2, 239--267. MR3215622
  • Menz, Georg; Otto, Felix. Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential. Ann. Probab. 41 (2013), no. 3B, 2182--2224. MR3098070
  • Otto, Felix; Reznikoff, Maria G. A new criterion for the logarithmic Sobolev inequality and two applications. J. Funct. Anal. 243 (2007), no. 1, 121--157. MR2291434
  • Procacci, Aldo; Scoppola, Benedetto. On decay of correlations for unbounded spin systems with arbitrary boundary conditions. J. Statist. Phys. 105 (2001), no. 3-4, 453--482. MR1871653
  • Royer, Gilles. An initiation to logarithmic Sobolev inequalities. Translated from the 1999 French original by Donald Babbitt. SMF/AMS Texts and Monographs, 14. American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2007. viii+119 pp. ISBN: 978-0-8218-4401-4; 0-8218-4401-6 MR2352327
  • Stroock, Daniel W.; Zegarliński, Bogusław. The logarithmic Sobolev inequality for continuous spin systems on a lattice. J. Funct. Anal. 104 (1992), no. 2, 299--326. MR1153990
  • Stroock, Daniel W.; Zegarliński, Bogusław. The logarithmic Sobolev inequality for discrete spin systems on a lattice. Comm. Math. Phys. 149 (1992), no. 1, 175--193. MR1182416
  • Sylvester, Garrett S. Inequalities for continuous-spin Ising ferromagnets. J. Statist. Phys. 15 (1976), no. 4, 327--341. MR0436856
  • Yoshida, Nobuo. The log-Sobolev inequality for weakly coupled lattice fields. Probab. Theory Related Fields 115 (1999), no. 1, 1--40. MR1715549
  • Yoshida, Nobuo. 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), no. 2, 223--243. MR1819124
  • Yoshida, Nobuo. Phase transition from the viewpoint of relaxation phenomena. Rev. Math. Phys. 15 (2003), no. 7, 765--788. MR2018287
  • Zegarlinski, Boguslaw. The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice. Comm. Math. Phys. 175 (1996), no. 2, 401--432. MR1370101
  • Zitt, Pierre-André. Functional inequalities and uniqueness of the Gibbs measure—from log-Sobolev to Poincaré. ESAIM Probab. Stat. 12 (2008), 258--272. MR2374641
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.