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Percolation beyond $$\mathbb{Z}^ d$$, many questions and a few answers. (English) Zbl 0890.60091
Summary: 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.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation
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