On the Distribution of a Two-Dimensional Random Walk with Restricted Angles
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910222858059776 |
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| author | Besser, Karl-Ludwig |
| author_facet | Besser, Karl-Ludwig |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Distribution of a Two-Dimensional Random Walk with Restricted Angles Besser, Karl-Ludwig Signal Processing Probability Applications 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. |
| title | On the Distribution of a Two-Dimensional Random Walk with Restricted Angles |
| topic | Signal Processing Probability Applications |
| url | https://arxiv.org/abs/2507.15475 |