An upper bound for the probability of visiting a distant point by critical branching random walk in ${\mathbb{Z}}^4$

In this paper, we study the probability of visiting a distant point $a\in $\mathbb{Z}$^4$ by critical branching random walk starting from the origin. We prove that this probability is bounded by $1\mathrm{/}(\mathrm{\mid }a{\mathrm{\mid }}^2\log \mathrm{\mid }a\mathrm{\mid })$ up to a constant.