论文信息 - On the random-cluster model II. The percolation model

On the random-cluster model II. The percolation model

Abstract The relationship among several criteria of large-range connectivity in an infinite percolation model is investigated. In particular, we establish the equivalence, under a non-trivial condition, between weak and strong large-range connectivity, related, respectively, with the probability that a vertex belongs to an infinite cluster and the probability that a vertex is connected with vertices “very far away”. Furthermore, it is shown that the role of infinity can, in a certain sense, be taken over by a supplementary vertex.

C. Fortuin | C. M. Fortuin

[1] C. Fortuin,et al. On the random-cluster model: I. Introduction and relation to other models , 1972 .

[2] D. Koenig. Theorie Der Endlichen Und Unendlichen Graphen , 1965 .

[3] J. W. Essam,et al. Some Cluster Size and Percolation Problems , 1961 .

[4] Michael E. Fisher,et al. Critical Probabilities for Cluster Size and Percolation Problems , 1961 .

[5] M. Fisher. Correlation Functions and the Coexistence of Phases , 1965 .

[6] S. Sherman,et al. General Griffiths' Inequalities on Correlations in Ising Ferromagnets , 1968 .

[7] Robert B. Griffiths,et al. Correlations in Ising Ferromagnets. I , 1967 .

[8] J. Hammersley. Percolation Processes: Lower Bounds for the Critical Probability , 1957 .

[9] Adriaan C. Zaanen,et al. An introduction to the theory of integration , 1959 .

[10] C. Fortuin,et al. Correlation inequalities on some partially ordered sets , 1971 .

[11] J. Doob. Stochastic processes , 1953 .