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arXiv · 1301.1165

Zebra-percolation on Cayley trees

D. Gandolfo·U. A. Rozikov·J. Ruiz
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Abstract

We consider Bernoulli (bond) percolation with parameter $p$ on the Cayley tree of order $k$. We introduce the notion of zebra-percolation that is percolation by paths of alternating open and closed edges. In contrast with standard percolation with critical threshold at $p_c= 1/k$, we show that zebra-percolation occurs between two critical values $p_{{\rm c},1}$ and $p_{{\rm c},2}$ (explicitly given). We provide the specific formula of zebra-percolation function.

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D. Gandolfo, U. A. Rozikov, J. Ruiz. 2013-01-07. Zebra-percolation on Cayley trees. https://arxiv.org/abs/1301.1165

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