Atypical Decay Rates for Atypical Heights in Random Recursive Trees
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908986028064768 |
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| author | Chen, Xinxin Ma, Heng |
| author_facet | Chen, Xinxin Ma, Heng |
| contents | We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows to infinity more slowly than any $n$-fold iterated logarithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20139 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Atypical Decay Rates for Atypical Heights in Random Recursive Trees Chen, Xinxin Ma, Heng Probability We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows to infinity more slowly than any $n$-fold iterated logarithm. |
| title | Atypical Decay Rates for Atypical Heights in Random Recursive Trees |
| topic | Probability |
| url | https://arxiv.org/abs/2604.20139 |