High-density percolation on the modified Bethe lattice.
basic_science · Level V
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- Record sourced from PubMed, PMID 31212449.
- Also identified by DOI 10.1103/PhysRevE.99.052109.
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Abstract
High-density percolation is the formation of a system spanning cluster of vertices with at least m occupied neighbors. We discuss high-density percolation on the modified Bethe lattice in terms of the theory of large random graphs with arbitrary degree distributions. Using the formalism of generating functions, we derive expressions for the cluster size distribution, the percolation threshold, the percolation probability, and the mean size of finite clusters. We show that the critical exponents β=γ=1. Additionally, numerical solutions and simulation results for the percolation probability and mean size of finite clusters are compared for illustration.