Universality for catalytic equations and fully parked trees
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909547557289984 |
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| author | Contat, Alice Curien, Nicolas |
| author_facet | Contat, Alice Curien, Nicolas |
| contents | We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree different from Aldous' Brownian tree recently introduced and studied by Bertoin, Curien and Riera. As a by-product of our study, we prove that positive non-linear polynomial equations involving a catalytic variable display a universal polynomial exponent $5/2$ at their singularity, confirming a conjecture by Chapuy, Schaeffer and Drmota & Hainzl. Compared to previous analytical works on the subject, our approach is probabilistic and exploits an underlying random walk hidden in the random tree model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality for catalytic equations and fully parked trees Contat, Alice Curien, Nicolas Probability Combinatorics We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree different from Aldous' Brownian tree recently introduced and studied by Bertoin, Curien and Riera. As a by-product of our study, we prove that positive non-linear polynomial equations involving a catalytic variable display a universal polynomial exponent $5/2$ at their singularity, confirming a conjecture by Chapuy, Schaeffer and Drmota & Hainzl. Compared to previous analytical works on the subject, our approach is probabilistic and exploits an underlying random walk hidden in the random tree model. |
| title | Universality for catalytic equations and fully parked trees |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2503.17348 |