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Coincidence of critical points in percolation problems. (English. Russian original) Zbl 0615.60096
Sov. Math., Dokl. 33, 856-859 (1986); translation from Dokl. Akad. Nauk SSSR 288, 1308-1311 (1986).
The article is devoted to the percolation problems on fairly general graphs with subexponential growth of a volume of a ball of radius R placed at any vertex. Under certain conditions the coincidence of two percolation thresholds is proved. Besides, some exponential and subexponential upper bounds on cluster size are established. One of the crucial points in the proof is using the FKG inequality.
Reviewer: V.Chulaevsky

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60E15 Inequalities; stochastic orderings