Parking on the Random Recursive Tree
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929660976168960 |
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| author | Contat, Alice Laulin, Lucile |
| author_facet | Contat, Alice Laulin, Lucile |
| contents | We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transition for the parking process appears at density $0$. We then identify the critical window for appearance of a positive flux of cars with high probability. In the case of binary car arrivals, this happens at density $ \log (n)^{-2+o(1)}$ where $n$ is the size of the tree. This is the first work that studies the parking process on trees with possibly large degree vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parking on the Random Recursive Tree Contat, Alice Laulin, Lucile Probability Combinatorics We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transition for the parking process appears at density $0$. We then identify the critical window for appearance of a positive flux of cars with high probability. In the case of binary car arrivals, this happens at density $ \log (n)^{-2+o(1)}$ where $n$ is the size of the tree. This is the first work that studies the parking process on trees with possibly large degree vertices. |
| title | Parking on the Random Recursive Tree |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2501.03195 |