Abstract
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.
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Foundation item: the National Natural Science Foundation of China (No. 10531070)
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Xu, Zh., Han, D. Infinite clusters in locally dependent percolation on ℤd . J. Shanghai Jiaotong Univ. (Sci.) 14, 626–628 (2009). https://doi.org/10.1007/s12204-009-0626-x
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DOI: https://doi.org/10.1007/s12204-009-0626-x