论文标题
在广义可见晶格点上随机行走
Random walks on generalized visible lattice points
论文作者
论文摘要
我们考虑随机步行者访问的飞机中广义可见晶格点的比例。我们的工作涉及三个方面随机步行中可见的晶格点：（1）沿曲线的广义可见性； （2）从多个观察点可见一个随机助行器； （3）多个随机步行者的同时可见性。此外，在多个随机步行者的情况下，我们发现了新现象：对于沿着大类曲线的可见性，对于任何数量的随机步行者，同时可见所有随机步行者的步骤比例几乎肯定比正常常数大。
We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random walker visible from multiple watchpoints; (3) simultaneous visibility of multiple random walkers. Moreover, we found new phenomenon in the case of multiple random walkers: for visibility along a large class of curves and for any number of random walkers, the proportion of steps at which all random walkers are visible simultaneously is almost surely larger than a positive constant.
