JournalsprimsVol. 42 , No. 1DOI 10.2977/prims/1166642060

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

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).