Abstract
We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on ℤd or ℤd × ℕ with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on ℤd or on a slab ℤd × {0,... K} and prove both that percolation occurs and that the infinite component is unique for V=ℤ2×{0,1} or larger.
Original language | English (US) |
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Pages (from-to) | 511-527 |
Number of pages | 17 |
Journal | Probability Theory and Related Fields |
Volume | 92 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1992 |
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty