Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 1 (1996), paper no. 8, 71-82.
Percolation Beyond $Z^d$, Many Questions And a Few Answers
A comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical value $p_c$ are given, and a simple planar example exhibiting uniqueness and non-uniqueness for different $p>p_c$ is analyzed. Numerous varied conjectures and problems are proposed, with the hope of setting goals for future research in percolation theory.
Electron. Commun. Probab., Volume 1 (1996), paper no. 8, 71-82.
Accepted: 8 October 1996
First available in Project Euclid: 25 January 2016
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Benjamini, Itai; Schramm, Oded. Percolation Beyond $Z^d$, Many Questions And a Few Answers. Electron. Commun. Probab. 1 (1996), paper no. 8, 71--82. doi:10.1214/ECP.v1-978. https://projecteuclid.org/euclid.ecp/1453756499