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VOL. 87 | 2021 Note on the maximal jump size in a continuum model of directed first passage percolation
Ryoki Fukushima

Editor(s) Yuzuru Inahama, Hirofumi Osada, Tomoyuki Shirai

## Abstract

In this note, we consider 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 positive 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.

## Information

Published: 1 January 2021
First available in Project Euclid: 20 January 2022

Digital Object Identifier: 10.2969/aspm/08710213

Subjects:
Primary: 60K37
Secondary: 60K35 , 82A51 , 82D30

Keywords: Directed polymer , first passage percolation , Ground states , random environment , zero temperature