Abstract
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.
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The author sincerely thanks the anonymous referee for valuable comments and suggestions.
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The author is partially supported by the National Natural Science Foundation of China (No. 12201346) and Shandong Provincial Foundation (No. 2022HWYQ-046 and No. ZR2022QA001).
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Lu, M. Visibility Properties Of Lattice Points In Multiple Random Walks. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01412-3
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DOI: https://doi.org/10.1007/s10474-024-01412-3