ON SOME PERCOLATION RESULTS OF J. M. HAMMERSLEY.
An examination is made of how much classical percolation theory on lattices can be extended to arbitrary graphs or even clutters of subsets of a finite set. In the process new short proofs of some theorems of J. M. Hammersley are obtained. The FKG inequality is used to get an upper bound for the percolation probability, and a lower bound is also derived.
Publication Source (Journal or Book title)
Journal of Applied Probability
Oxley, J., & Welsh, D. (1979). ON SOME PERCOLATION RESULTS OF J. M. HAMMERSLEY.. Journal of Applied Probability, 16 (3), 526-540. https://doi.org/10.1017/S0021900200107673