Visibility Properties Of Lattice Points In Multiple Random Walks

This paper concerns the visibility properties of lattice pointsin multiple random walks on \(\mathbb{N}^k\) ${\mathbb{N}}^k$ , where \(k\geq 2\) $k\ge 2$ is an integer. We study two aspectsof the visibility: simultaneous visibility in multiple random walkers; andthat only some of these walkers are visible. Combining tools from number theoryand probability theory, we prove the corresponding densities of the above twoparts.