2021/03/09 by Bernardo N. B. de Lima, Réka Szabó, de Lima, Bernardo N. B. +3 · 1 citation
Mathematics · Physics and Astronomy · #60K35 #82B43 #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2103.05316
openalex publication_date 2021/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an inhomogeneous oriented percolation model introduced by de Lima, Rolla and Valesin. In this model, the underlying graph is an oriented rooted tree in which each vertex points to each of its d children with `short' edges, and in addition, each vertex points to each of its dk descendant at a fixed distance k with `long' edges. A bond percolation process is then considered on this graph, with the prescription that independently, short edges are open with probability p and long edges are open with probability q. We study the behavior of the critical curve qc(p): we find the first two terms in the expansion of qc(p) as k → ∞, and prove that the critical curve lies strictly above the critical curve of a related branching process, in the relevant parameter region. We also prove limit theorems for the percolation cluster in the supercritical, subcritical and critical regimes.