A note on Pólya urns: the winner may lead all the time
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908411177730048 |
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| author | Janson, Svante |
| author_facet | Janson, Svante |
| contents | Consider a Pólya urn where a drawn ball of colour $i$ is replaced together with a fixed number $m_i$ of balls of the same colour. We give a simple proof that if, for example, there are two colours and the urn starts with more balls of colour 1 than 2, and $m_1\ge m_2$, then there is a positive probability that there always will be more balls of colour 1 than colour 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on Pólya urns: the winner may lead all the time Janson, Svante Probability 60C05 Consider a Pólya urn where a drawn ball of colour $i$ is replaced together with a fixed number $m_i$ of balls of the same colour. We give a simple proof that if, for example, there are two colours and the urn starts with more balls of colour 1 than 2, and $m_1\ge m_2$, then there is a positive probability that there always will be more balls of colour 1 than colour 2. |
| title | A note on Pólya urns: the winner may lead all the time |
| topic | Probability 60C05 |
| url | https://arxiv.org/abs/2506.14859 |