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


  • Aldous, David; Diaconis, Persi. The asymmetric one-dimensional constrained Ising model: rigorous results. J. Statist. Phys. 107 (2002), no. 5-6, 945--975. MR1901508
  • Bhatnagar, Nayantara; Caputo, Pietro; Tetali, Prasad; Vigoda, Eric. Analysis of top-swap shuffling for genome rearrangements. Ann. Appl. Probab. 17 (2007), no. 4, 1424--1445. MR2344312
  • Oriane Blondel. Front progression for the East model., math.PR, December 2012.
  • Cancrini, N.; Martinelli, F.; Roberto, C.; Toninelli, C. Kinetically constrained spin models. Probab. Theory Related Fields 140 (2008), no. 3-4, 459--504. MR2365481
  • Caputo, Pietro; Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan; Toninelli, Fabio Lucio. The shape of the $(2+1)\roman{d}$ SOS surface above a wall. C. R. Math. Acad. Sci. Paris 350 (2012), no. 13-14, 703--706. MR2971384
  • Caputo, Pietro; Martinelli, Fabio; Toninelli, Fabio Lucio. Convergence to equilibrium of biased plane partitions. Random Structures Algorithms 39 (2011), no. 1, 83--114. MR2839986
  • Chung, Fan; Diaconis, Persi; Graham, Ronald. Combinatorics for the East model. Adv. in Appl. Math. 27 (2001), no. 1, 192--206. MR1835679
  • R. Durrett. Lecture notes on particle systems and percolation. Lecture Notes in Mathematics, (1608), 1995.
  • Durrett, Richard. Oriented percolation in two dimensions. Ann. Probab. 12 (1984), no. 4, 999--1040. MR0757768
  • Faggionato, A.; Martinelli, F.; Roberto, C.; Toninelli, C. Aging through hierarchical coalescence in the East model. Comm. Math. Phys. 309 (2012), no. 2, 459--495. MR2864800
  • A. Faggionato, F. Martinelli, C. Roberto, and C. Toninelli. Universality in one dimensional hierarchical coalescence processes. Ann. Probab., 40(4):1377--1435, 2012.
  • Kordzakhia, George; Lalley, Steven P. Ergodicity and mixing properties of the northeast model. J. Appl. Probab. 43 (2006), no. 3, 782--792. MR2274800
  • Levin, David A.; Peres, Yuval; Wilmer, Elizabeth L. Markov chains and mixing times. With a chapter by James G. Propp and David B. Wilson. American Mathematical Society, Providence, RI, 2009. xviii+371 pp. ISBN: 978-0-8218-4739-8 MR2466937
  • Liggett, Thomas M. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231
  • Liggett, Thomas M. Stochastic interacting systems: contact, voter and exclusion processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 324. Springer-Verlag, Berlin, 1999. xii+332 pp. ISBN: 3-540-65995-1 MR1717346
  • F~Martinelli and C~Toninelli. Kinetically constrained spin models on trees. Annals of Applied Probability, in press, 2012.
  • Roberto Oliveira. Mixing and hitting times for finite markov chains. Electron. J. Probab., 17, 2012.
  • Y~Peres and A~Sly. Mixing of the upper triangular matrix walk. Probability Theory and Related Fields, pages 1--11, 2011.
  • Yuval Peres and Perla Sousi. Mixing times are hitting times of large sets. 2011.
  • F. Ritort and P. Sollich. Glassy dynamics of kinetically constrained models. Advances in Physics, 52(4):219--342, 2003.
  • Saloff-Coste, Laurent. Lectures on finite Markov chains. Lectures on probability theory and statistics (Saint-Flour, 1996), 301--413, Lecture Notes in Math., 1665, Springer, Berlin, 1997. MR1490046
  • P. Sollich and M.R. Evans. Glassy dynamics in the asymmetrically constrained kinetic ising chain. Phys. Rev. E, page 031504, 2003.
  • Toninelli, Cristina; Biroli, Giulio. A new class of cellular automata with a discontinuous glass transition. J. Stat. Phys. 130 (2008), no. 1, 83--112. MR2375957
  • Valiant, Paul. Linear bounds on the North-East model and higher-dimensional analogs. Adv. in Appl. Math. 33 (2004), no. 1, 40--50. MR2064356

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