Local limits of conditioned marked Galton Watson trees
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915515851603968 |
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| author | Abraham, Romain Boulal, Sonia Debs, Pierre |
| author_facet | Abraham, Romain Boulal, Sonia Debs, Pierre |
| contents | We consider a Galton-Watson tree where each node is marked independently of each others with a probability depending on its outdegree. We give a complete picture of the local convergence of critical or sub-critical marked Galton-Watson trees conditioned on having a large number of marks. In the critical and sub-critical generic case, the limit is a random marked tree with an infinite spine, named marked Kesten's tree. We focus also on the non-generic case, where the local limit is a random marked tree with a node with infinite out-degree. This case corresponds to the so-called marked condensation phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local limits of conditioned marked Galton Watson trees Abraham, Romain Boulal, Sonia Debs, Pierre Probability We consider a Galton-Watson tree where each node is marked independently of each others with a probability depending on its outdegree. We give a complete picture of the local convergence of critical or sub-critical marked Galton-Watson trees conditioned on having a large number of marks. In the critical and sub-critical generic case, the limit is a random marked tree with an infinite spine, named marked Kesten's tree. We focus also on the non-generic case, where the local limit is a random marked tree with a node with infinite out-degree. This case corresponds to the so-called marked condensation phenomenon. |
| title | Local limits of conditioned marked Galton Watson trees |
| topic | Probability |
| url | https://arxiv.org/abs/2509.18804 |