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.
A central limit theorem for critical first-passage percolation in two dimensions.Probability Theory and Related Fields, 107:137–160
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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.