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

  • Aizenman, M.; Holley, R. Rapid convergence to equilibrium of stochastic Ising models in the Dobrushin Shlosman regime. Percolation theory and ergodic theory of infinite particle systems (Minneapolis, Minn., 1984–1985), 1--11, IMA Vol. Math. Appl., 8, Springer, New York, 1987. MR0894538
  • Chazottes, Jean-René; Redig, Frank; Völlering, Florian. The Poincaré inequality for Markov random fields proved via disagreement percolation. Indag. Math. (N.S.) 22 (2011), no. 3-4, 149--164. MR2853604
  • Dobrušin, R. L. Description of a random field by means of conditional probabilities and conditions for its regularity. (Russian) Teor. Verojatnost. i Primenen 13 1968 201--229. MR0231434
  • Holley, Richard. Possible rates of convergence in finite range, attractive spin systems. Particle systems, random media and large deviations (Brunswick, Maine, 1984), 215--234, Contemp. Math., 41, Amer. Math. Soc., Providence, RI, 1985. MR0814713
  • Holley, Richard; Stroock, Daniel. Logarithmic Sobolev inequalities and stochastic Ising models. J. Statist. Phys. 46 (1987), no. 5-6, 1159--1194. MR0893137
  • Kesten, Harry. Aspects of first passage percolation. École d'été de probabilités de Saint-Flour, XIV—1984, 125--264, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876084
  • Liggett, Thomas M. Interacting particle systems. Reprint of the 1985 original. Classics in Mathematics. Springer-Verlag, Berlin, 2005. xvi+496 pp. ISBN: 3-540-22617-6 MR2108619
  • Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan; Toninelli, Fabio Lucio. Quasi-polynomial mixing of the 2D stochastic Ising model with "plus'' boundary up to criticality. J. Eur. Math. Soc. (JEMS) 15 (2013), no. 2, 339--386. MR3017041
  • Martinelli, F.; Olivieri, E. Approach to equilibrium of Glauber dynamics in the one phase region. II. The general case. Comm. Math. Phys. 161 (1994), no. 3, 487--514. MR1269388
  • Röckner, Michael; Wang, Feng-Yu. Weak Poincaré inequalities and $L^ 2$-convergence rates of Markov semigroups. J. Funct. Anal. 185 (2001), no. 2, 564--603. MR1856277
  • Shlosman, S. B. Uniqueness and half-space nonuniqueness of Gibbs states in Czech models. (Russian) Teoret. Mat. Fiz. 66 (1986), no. 3, 430--444. MR0847435
  • van den Berg, J.; Maes, C. Disagreement percolation in the study of Markov fields. Ann. Probab. 22 (1994), no. 2, 749--763. MR1288130
  • Yoshida, Nobuo. Relaxed criteria of the Dobrushin-Shlosman mixing condition. J. Statist. Phys. 87 (1997), no. 1-2, 293--309. MR1453741
Bookmark and Share


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