论文标题
在曼哈顿弹球问题上
On the Manhattan pinball problem
论文作者
论文摘要
我们考虑了定期的曼哈顿晶格，其交替方向向北和东西向。以概率$ 0 <p <1 $独立地将障碍物放置在顶点上。粒子在晶格方向后以单位速度在边缘上移动，并且仅在遇到阻塞时才会转动。问题在于，对于$ p $的哪个值是粒子的轨迹，几乎肯定是关闭的。我们以$ p> \ frac {1} {2} - \ varepsilon $和一些$ \ varepsilon> 0 $的价格证明了这一点。
We consider the periodic Manhattan lattice with alternating orientations going north-south and east-west. Place obstructions on vertices independently with probability $0<p<1$. A particle is moving on the edges with unit speed following the orientation of the lattice and it will turn only when encountering an obstruction. The problem is that for which value of $p$ is the trajectory of the particle closed almost surely. We prove this for $p>\frac{1}{2}-\varepsilon$ with some $\varepsilon>0$.
