  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.
