Disagreement Percolation in the Study of Markov Fields
| Autor: | Christian Maes, van den Rob Berg |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Statistics and Probability
(optimal) coupling Markov chain uniqueness condition for Gibbs states 82B43 Percolation Boundary (topology) Gibbs state Coupling (probability) Combinatorics 60K35 Condensed Matter::Statistical Mechanics Markov fields 82B26 Ising model Uniqueness Boundary value problem Statistical physics Statistics Probability and Uncertainty 82B05 Mathematics |
| Zdroj: | Annals of Probability, 22(2), 749-763 Ann. Probab. 22, no. 2 (1994), 749-763 |
| ISSN: | 0091-1798 |
| DOI: | 10.1214/aop/1176988728 |
| Popis: | Recently, one of the authors (van den Berg) has obtained a uniqueness condition for Gibbs measures, in terms of disagreement percolation involving two independent realizations. In the present paper we study the dependence of Markov fields on boundary conditions by taking a more suitable coupling. This coupling leads to a new uniqueness condition, which improves the one mentioned above. We also compare it with the Dobrushin uniqueness condition. In the case of the Ising model, our coupling shares certain properties with the Fortuin-Kasteleyn representation: It gives an explicit expression of the boundary effect on a certain vertex in terms of percolation-like probabilities. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|