Crossing bridges between percolation models and Bienaymé-Galton-Watson trees
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913660554706944 |
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| author | Blancas, Airam Fittipaldi, María Clara Hernández-Torres, Saraí |
| author_facet | Blancas, Airam Fittipaldi, María Clara Hernández-Torres, Saraí |
| contents | In this survey, we explore the connections between two areas of probability: percolation theory and population genetic models. Our first goal is to highlight a construction on Galton-Watson trees, which has been described in two different ways: Bernoulli bond percolation and neutral mutations. Next, we introduce a novel connection between the Divide-and-Color percolation model and a particular multi-type Galton-Watson tree. We provide a gentle introduction to these topics while presenting an overview of the results that connect them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Crossing bridges between percolation models and Bienaymé-Galton-Watson trees Blancas, Airam Fittipaldi, María Clara Hernández-Torres, Saraí Probability 60J80, 92D25, 60K35, 82B43 In this survey, we explore the connections between two areas of probability: percolation theory and population genetic models. Our first goal is to highlight a construction on Galton-Watson trees, which has been described in two different ways: Bernoulli bond percolation and neutral mutations. Next, we introduce a novel connection between the Divide-and-Color percolation model and a particular multi-type Galton-Watson tree. We provide a gentle introduction to these topics while presenting an overview of the results that connect them. |
| title | Crossing bridges between percolation models and Bienaymé-Galton-Watson trees |
| topic | Probability 60J80, 92D25, 60K35, 82B43 |
| url | https://arxiv.org/abs/2411.09621 |