English

Maximal edge-traversal time in First Passage Percolation

Probability 2021-02-22 v9

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.

Keywords

Cite

@article{arxiv.1605.04787,
  title  = {Maximal edge-traversal time in First Passage Percolation},
  author = {Shuta Nakajima},
  journal= {arXiv preprint arXiv:1605.04787},
  year   = {2021}
}

Comments

33 pages, 10 figures

R2 v1 2026-06-22T14:01:43.167Z