Print Email Facebook Twitter On the Uniqueness of the Infinite Occupied Cluster in Dependent Two- Dimensional Site Percolation Title On the Uniqueness of the Infinite Occupied Cluster in Dependent Two- Dimensional Site Percolation Author Gandolfi, A. Keane, M. Russo, L. Faculty Electrical Engineering, Mathematics and Computer Science Department Applied mathematics Date 1988 Abstract We consider dependent site percolation on the two-dimensional square lattice, the underlying probability measure being invariant and ergodic under each of the translations and invariant under axis reflections. If this measure satisfies the FKG condition and if percolation occurs, then we show that the infinite occupied cluster is unique with probability 1, and that all vacant star-clusters are finite. Subject Open Access To reference this document use: http://resolver.tudelft.nl/uuid:9d6051ad-22bf-45ab-bb44-410e5410e2e9 DOI https://doi.org/10.1214/aop/1176991681 Publisher Institute of Mathematical Statistics Source Annals Probability. Volume 16, Number 3 (1988), 1147-1157. Part of collection Institutional Repository Document type journal article Rights (c) Institute of Mathematical Statistics Files PDF Gandolfi1euclid.pdf 901.65 KB Close viewer /islandora/object/uuid:9d6051ad-22bf-45ab-bb44-410e5410e2e9/datastream/OBJ/view