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

  1. N. Bhatnagar, E. Maneva, A computational method for bounding the probability of reconstruction on trees, preprint 2009.
  2. C. Borgs, J.T. Chayes, E. Mossel, S.Roch,The Kesten-Stigum reconstruction bound is tight for roughly symmetric binary channels, 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 518-530 (2006).
  3. J. B. Martin,Reconstruction thresholds on regular trees, Discrete Random Walks, DWR '03, eds. C. Banderier and C. Krattenthaler,Discrete Mathematics and Theoretical Computer Science Proceedings AC, 191-204 (2003). MR2042387 (2005b:60019)
  4. P. M. Bleher, J. Ruiz, V.A. Zagrebnov, On the purity of limiting Gibbs state for the Ising model on the Bethe lattice,J. Stat. Phys. textbf{79}, 473-482 (1995). MR1325591 (96d:82009)
  5. M. Formentin, C. Kulske, On the Purity of the free boundary condition Potts measure on random trees, Stochastic Processes and their Applications 119, Issue 9, 2992-3005 (2009). MR2554036
  6. H. O. Georgii, Gibbs measures and phase transitions, de Gruyter Studies in Mathematics 9,Walter de Gruyter & Co., Berlin(1988). MR0956646 (89k:82010)
  7. A. Gerschenfeld, A. Montanari, Reconstruction for models on random graphs, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 194-204 (2007).
  8. D. Ioffe, A note on the extremality of the disordered state for the Ising model on the Bethe lattice, Lett. Math. Phys. 37, 137-143 (1996).MR1391195 (97e:82004)
  9. D. Ioffe, Extremality of the disordered state for the Ising model ongeneral trees,Trees (Versailles), 3-14, Progr. Probab.40,Birkhauser, Basel (1996).MR1439968 (98j:82013)
  10. R. Lyons, Phase transitions on nonamenable graphs.In: Probabilistic techniques in equilibrium and nonequilibrium statistical physics,J. Math. Phys. 41 no. 3, 1099-1126(2000). MR1757952 (2001c:82028)
  11. S. Janson, E. Mossel,Robust reconstruction on trees is determined by the second eigenvalue, Ann. Probab. 32 no. 3B, 2630-2649 (2004). MR2078553 (2005h:60296)
  12. E. Mossel, Reconstruction on trees: Beating the second eigenvalue, Ann. Appl. Prob. 11 285-300 (2001).MR1825467 (2003d:90010)
  13. E. Mossel, Y.Peres,Information flow on trees, The Annals of Applied Probability13 no. 3, 817-844 (2003). MR1994038 (2004e:60143)
  14. R. Pemantle, Y. Peres, The critical Ising model on trees, concave recursions and nonlinear capacity,preprint, arXiv:math/0503137v2 [math.PR] (2006),to appear in The Annals of Probability.
  15. F. Martinelli, A. Sinclair, D. Weitz,Fast mixing for independents sets, colorings and other model on trees,Comm. Math. Phys. 250 no. 2, 301-334 (2004). MR2094519 (2005j:82052)
  16. M. Mezard, A. Montanari,Reconstruction on trees and spin glass transition, J. Stat. Phys. 124 no. 6, 1317-1350 (2006). MR2266446 (2008b:82024)
  17. A. Sly,Reconstruction of symmetric Potts models, preprint, arXiv:0811.1208 [math.PR] (2008).
Bookmark and Share


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