A lower bound for pc in range-R bond percolation in four, five and six dimensions

Jieliang Hong

Stochastic Processes and their Applications, 2025, vol. 185, issue C

Abstract: For the range-R bond percolation in d=4,5,6, we obtain a lower bound for the critical probability pc for R large, agreeing with the conjectured asymptotics and thus complementing the corresponding results of Van der Hofstad and Sakai (2005) for d>6, and Frei and Perkins (2016), Hong (2023) for d≤3. The lower bound proof is completed by showing the extinction of the associated SIR epidemic model. To prove the extinction of the SIR epidemics, we introduce a refined model of the branching random walk, called a self-avoiding branching random walk, whose total range dominates that of the SIR epidemic process.

Keywords: Long range bond percolation; SIR epidemic; Branching random walk (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104637

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