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.
Limit theorems for high-dimensional Betti numbers in the multiparameter random simplicial complexes.Stochastic Processes and their Applications, 186:104641
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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.