{"ID":2892183,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15475","arxiv_id":"2507.15475","title":"On the Distribution of a Two-Dimensional Random Walk with Restricted Angles","abstract":"In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in signal processing. In particular, we derive the exact joint and marginal distributions for two steps, numerical solutions for a general number of steps, and approximations for a large number of steps. Furthermore, we provide an exact characterization of the support for an arbitrary number of steps. The results in this work provide a reference for future work involving such problems.","short_abstract":"In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in signal processing. In particular, we derive the exact joint and marginal distribut...","url_abs":"https://arxiv.org/abs/2507.15475","url_pdf":"https://arxiv.org/pdf/2507.15475v2","authors":"[\"Karl-Ludwig Besser\"]","published":"2025-07-21T10:27:49Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"math.PR\",\"stat.AP\"]","methods":"[]","has_code":false}