摘要
Techniques of Burton-Keane,developed earlier for independent percolation on Zd,are adapted to the setting of locally dependent percolation on Zd for d 2.The main result of this paper is a uniqueness theorem,that there exists almost surely a unique infinite out-cluster in locally dependent percolation on Zd,under the finite energy condition.
Techniques of Burton-Keane, developed earlier for independent percolation on Z^d, are adapted to the setting of locally dependent percolation on Z^d for d ≥ 2. The main result of this paper is a uniqueness theorem, that there exists almost surely a unique infinite out-cluster in locally dependent percolation on Z^d, under the finite energy condition.
基金
the National Natural Science Foundation of China (No.10531070)
