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arXiv · 2009.03609

Random walks on generalized visible lattice points

Kui Liu·Xianchang Meng
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Abstract

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.

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Kui Liu, Xianchang Meng. 2020-09-08. Random walks on generalized visible lattice points. https://arxiv.org/abs/2009.03609

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