Visibility Properties Of Lattice Points In Multiple Random Walks

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