JournalsprimsVol. 42, No. 1pp. 101–116

Remarks on Central Limit Theorems for the Number of Percolation Clusters

  • Nobuaki Sugimine

    ERATO, JST, Tokyo, Japan
  • Masato Takei

    Kobe University, Japan
Remarks on Central Limit Theorems for the Number of Percolation Clusters cover
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Abstract

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. 101–116

DOI 10.2977/PRIMS/1166642060