An upper bound for p_c in range-R bond percolation in two and three dimensions

2021/07/29 by Jieliang Hong, Hong, Jieliang
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2107.14173

openalex publication_date 2021/07/29 · openalex created_date 2023/09/03 · openalex updated_date 2026/07/28

Abstract

An upper bound for the critical probability of long range bond percolation in d=2 and d=3 is obtained by connecting the bond percolation with the SIR epidemic model, thus complementing the lower bound result in Frei and Perkins arXiv:arch-ive/1603.04130. A key ingredient is that we establish a uniform bound for the local times of branching random walk by calculating their exponential moments and by using the discrete versions of Tanaka's formula and Garsia's Lemma.

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