Uniqueness thresholds on trees versus graphs

Annals of Applied Probability

Volumn 18, Issue 5, 2008, Pages 1897-1909

  Sly, Allan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Potts model; Uniqueness

Indexed keywords

EID: 63049112024     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/07-AAP508     Document Type: Article

References (10)

1. BANDYOPADHYAY, A. and GAMARNIK, D. (2006). Counting without sampling: New algorithms for enumeration problems using statistical physics. In SODA'06: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm 890-899. ACM, New York.
2. BRIGHTWELL, G., HÄGGSTRÖM, O. and WINKLER, P. (1999). Nonmonotonic behavior in hard-core and Widom-Rowlinson models. J. Statist. Phys. 94 415-435. MR1675359
3. DYER, M., SINCLAIR, A., VIGODA, E. and WEITZ, D. (2004). Mixing in time and space for lattice spin systems: A combinatorial view. Random Structures Algorithms 24 461-479. MR2060631
4. GOLDBERG, L. A., MARTIN, R. and PATERSON, M. (2004). Strong spatial mixing for lattice graphs with fewer colours. In FOCS'04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS'04) 562-571.
5. JUNG, K. and SHAH, D. Inference in binary pair-wise Markov random fields through self-avoiding walks. ArXiv Computer Science e-prints. Available at http://arxiv.org/abs/cs.AI/ 0610111v2.
6. MARTINELLI, F. (1999). Lectures on Glauber dynamics for discrete spin models. In Lectures on Probability Theory and Statistics (Saint-Flour, 1997). Lecture Notes in Mathematics 171793-191. Springer, Berlin. MR1746301
7. MOSSEL, E. (2006). Personal communication.
8. SCOTT, A. D. and SOKAL, A. D. (2005). The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma. J. Statist. Phys. 118 1151-1261. MR2130890
9. SOKAL, A. D. (2001). A personal list of unsolved problems concerning lattice gases and antiferromagnetic Potts models. Markov Process. Related Fields 1 21-38. MR1835744
10. WEITZ, D. (2006). Counting independent sets up to the tree threshold. In STOC'06: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing 140-149. MR2277139