Abstract
In this paper, we study the maximal edge-traversal time on optimal paths in First-passage percolation on the lattice 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 depending on the tail of the edge distribution.
Funding Statement
This research is partially supported by JSPS KAKENHI 16J04042 and Kyoto University Top Global University Project.
Acknowledgments
I would like to thank Professor Ryoki Fukushim giving me a plenty of helpful advice, encouraging me to carry out the research. I also would like to express my gratitude to Professor Antonio Auffinger for suggesting me this problem and introducing the idea of the arguments in [3]. I would like to show my appreciation to Professor Takashi Kumagai for a lot of advice and support. I am indebted to an anonymous reviewer of an earlier paper for providing insightful comments.
Citation
Shuta Nakajima. "Maximal edge-traversal time in First-passage percolation." Electron. J. Probab. 27 1 - 32, 2022. https://doi.org/10.1214/22-EJP746
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