Critical beta-splitting, via contraction
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909904087810048 |
|---|---|
| author | Kolesnik, Brett |
| author_facet | Kolesnik, Brett |
| contents | The critical beta-splitting tree, introduced by Aldous, is a Markov branching phylogenetic tree. Aldous and Pittel recently proved, amongst other results, a central limit theorem for the height of a random leaf. We give an alternative proof, via contraction methods for random recursive structures. These methods were developed by Neininger and Rüschendorf, motivated by Pittel's article "Normal convergence problem? Two moments and a recurrence may be the clues." Aldous and Pittel estimated the leading order terms in the first two moments. More recently, Aldous and Janson obtained an asymptotic expansion for the average height. We show that a central limit theorem follows, and bound the distance to normality. Our results also apply to the continuous version of the model, in which branching times are exponential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical beta-splitting, via contraction Kolesnik, Brett Probability Combinatorics 05C05, 60F05, 60C05, 60J90, 92B10 The critical beta-splitting tree, introduced by Aldous, is a Markov branching phylogenetic tree. Aldous and Pittel recently proved, amongst other results, a central limit theorem for the height of a random leaf. We give an alternative proof, via contraction methods for random recursive structures. These methods were developed by Neininger and Rüschendorf, motivated by Pittel's article "Normal convergence problem? Two moments and a recurrence may be the clues." Aldous and Pittel estimated the leading order terms in the first two moments. More recently, Aldous and Janson obtained an asymptotic expansion for the average height. We show that a central limit theorem follows, and bound the distance to normality. Our results also apply to the continuous version of the model, in which branching times are exponential. |
| title | Critical beta-splitting, via contraction |
| topic | Probability Combinatorics 05C05, 60F05, 60C05, 60J90, 92B10 |
| url | https://arxiv.org/abs/2404.16021 |