  We consider the Lorentz mirror model and the Manhattan model on the
even-width cylinder $\mathbb{Z} \times (\mathbb{Z}/2n\mathbb{Z})
=\{(x,y):x,y\in \mathbb{Z}, 1\leq y\leq 2n\}$. For both models, we show that
for large enough $n$, with high probability, any trajectory of light starting
from the section $x=0$ is contained in the region $|x|\leq O(n^{10})$.
