Critical Self-Similar Markov Trees
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910056161738752 |
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| author | Curien, Nicolas Hu, Xingjian Qian, Dongjian |
| author_facet | Curien, Nicolas Hu, Xingjian Qian, Dongjian |
| contents | Recently introduced and studied in arXiv:2407.07888, a self-similar Markov tree (ssMt) is a random decorated tree that vastly generalises the fragmentation tree. We study here the critical case that was left aside in arXiv:2407.07888. Borrowing techniques from branching random walk, in particular the recent result of Aïdékon--Hu--Shi arXiv:2409.01048, we can complete the picture by constructing critical ssMt, computing their fractal dimension and studying their associated harmonic and length measures using spinal decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16408 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical Self-Similar Markov Trees Curien, Nicolas Hu, Xingjian Qian, Dongjian Probability 60J80, 60G18, 60G51 Recently introduced and studied in arXiv:2407.07888, a self-similar Markov tree (ssMt) is a random decorated tree that vastly generalises the fragmentation tree. We study here the critical case that was left aside in arXiv:2407.07888. Borrowing techniques from branching random walk, in particular the recent result of Aïdékon--Hu--Shi arXiv:2409.01048, we can complete the picture by constructing critical ssMt, computing their fractal dimension and studying their associated harmonic and length measures using spinal decomposition. |
| title | Critical Self-Similar Markov Trees |
| topic | Probability 60J80, 60G18, 60G51 |
| url | https://arxiv.org/abs/2603.16408 |