We consider percolation problems on regular trees and some pre-fractal graphs. Central limit theorems for the number of open clusters in a ﬁnite box are obtained. n For regular trees and some classes of Sierpiński carpet lattices, we can prove the central limit theorems for all p ∈ (0, 1).
Cite this article
Nobuaki Sugimine, Masato Takei, Remarks on Central Limit Theorems for the Number of Percolation Clusters. Publ. Res. Inst. Math. Sci. 42 (2006), no. 1, pp. 101–116DOI 10.2977/PRIMS/1166642060