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arXiv · 1912.11728

Note on the maximal jump size in a continuum model of directed first passage percolation

Ryoki Fukushima
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Abstract

In this note, we study the directed first passage percolation introduced in [F. Comets, R. Fukushima, S. Nakajima and N. Yoshida: Journal of Statistical Physics, 161-(3), 577-597 (2015)]. It is proved that the shortest path from the origin to the $n$-th hyperplane makes a jump larger than a small power of $\log n$. Some numerical results are also provided, which indicates that the maximal jump size is much larger in a certain parameter region.

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Ryoki Fukushima. 2019-12-25. Note on the maximal jump size in a continuum model of directed first passage percolation. https://doi.org/10.2969/aspm%2F08710213

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