Central limit theorems hold for cluster counts K_r and stationary percolation functionals including Betti numbers on quasi-transitive subexponentially growing graphs and amenable Cayley graphs with left-orderable subgroups.
Percolation beyondZd, many questions and a few answers.Electronic Communications in Probability, 1:71–82
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Topology of Percolation Clusters: Central Limit Theorems beyond the Lattice
Central limit theorems hold for cluster counts K_r and stationary percolation functionals including Betti numbers on quasi-transitive subexponentially growing graphs and amenable Cayley graphs with left-orderable subgroups.