The coalescent of a sample from a linear-fractional branching process
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912443157970944 |
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| author | Cardona-Tobón, Natalia Palau, Sandra |
| author_facet | Cardona-Tobón, Natalia Palau, Sandra |
| contents | In this article, we focus on Bienaymé-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli sampling, where each individual is selected independently with a given probability, or through uniform sampling, where a fixed number of individuals are chosen uniformly at random. We analyze the genealogical trees generated by the sampled individuals. In particular, we establish a relationship between the distributions of the trees resulting from the two sampling schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The coalescent of a sample from a linear-fractional branching process Cardona-Tobón, Natalia Palau, Sandra Probability 60J80, 60J85, 62M20, 92D25 In this article, we focus on Bienaymé-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli sampling, where each individual is selected independently with a given probability, or through uniform sampling, where a fixed number of individuals are chosen uniformly at random. We analyze the genealogical trees generated by the sampled individuals. In particular, we establish a relationship between the distributions of the trees resulting from the two sampling schemes. |
| title | The coalescent of a sample from a linear-fractional branching process |
| topic | Probability 60J80, 60J85, 62M20, 92D25 |
| url | https://arxiv.org/abs/2506.17470 |