  Let $\mathcal{U}$ be the uniform spanning tree on $\mathbb{Z}^3$, whose
probability law is denoted by $\mathbf{P}$. For $\mathbf{P}$-a.s. realization
of $\mathcal{U}$, the recurrence of the the simple random walk on $\mathcal{U}$
is proved in [5] and it is also demonstrated in [8] that two independent simple
random walks on $\mathcal{U}$ collide infinitely often. In this article, we
will give a quantitative estimate on the number of collisions of two
independent simple random walks on $\mathcal{U}$, which provides another proof
of the infinite collision property of $\mathcal{U}$.
