Critical trees are neither too short nor too fat
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910856085766144 |
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| author | Addario-Berry, Louigi Donderwinkel, Serte Kortchemski, Igor |
| author_facet | Addario-Berry, Louigi Donderwinkel, Serte Kortchemski, Igor |
| contents | We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaymé trees. Our bounds are optimal at this level of generality. We also obtain precise asymptotics for offspring distributions within the domain of attraction of a Cauchy distribution, under a local regularity assumption. Finally, we pose some questions on the possible asymptotic behaviours of the height and width of critical size-conditioned Bienaymé trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06163 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Critical trees are neither too short nor too fat Addario-Berry, Louigi Donderwinkel, Serte Kortchemski, Igor Probability Combinatorics 05C05, 60C05, 60J80 We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaymé trees. Our bounds are optimal at this level of generality. We also obtain precise asymptotics for offspring distributions within the domain of attraction of a Cauchy distribution, under a local regularity assumption. Finally, we pose some questions on the possible asymptotic behaviours of the height and width of critical size-conditioned Bienaymé trees. |
| title | Critical trees are neither too short nor too fat |
| topic | Probability Combinatorics 05C05, 60C05, 60J80 |
| url | https://arxiv.org/abs/2311.06163 |