Cluster Expansion of the Percolation Probability on a Caley Tree
DOI:
https://doi.org/10.52575/2687-0959-2025-57-4-298-305Keywords:
Bernoulli’s Random Field, Branching Markov Chain, Supercritical Regime, Percolation Threshold, Cluster ExpansionAbstract
The Bernoulli uniform random field on the infinite uniform Caley tree with the vertex degree s = 3 is investigated. For this graph, the percolation probability P (c) of the random field from a marked graph vertex to infinity is studied, where it is a function on the vertex filling c. The famous cluster decomposition of the function
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