Maximal edge-traversal time in First Passage Percolation

2016/05/16 by Shuta Nakajima, Nakajima, Shuta
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.1605.04787

openalex publication_date 2016/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the maximal edge-traversal time (simply we call maximal weight hereafter) on the optimal paths in the first passage percolation for several edge distributions, including the Pareto and Weibull distributions. It is known to be unbounded when the edge distribution has unbounded support [J. van den Berg and H. Kesten. Inequalities for the time constant in first-passage percolation. Ann. Appl. Probab. 56-80, 1993]. We determine the order of the growth up to a multiplicative constant.

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