Comparison of limit shapes for Bernoulli first-passage percolation

2022/05/28 by Naoki Kubota, Masato Takei, Kubota, Naoki +1
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2205.14355

openalex publication_date 2022/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Bernoulli first-passage percolation on the d-dimensional hypercubic lattice with d ≥ 2. The passage time of edge e is 0 with probability p and 1 with probability 1-p, independently of each other. Let p_c be the critical probability for percolation of edges with passage time 0. When 0≤ p

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