Burning Random Trees
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916573137076224 |
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| author | Devroye, Luc Eide, Austin Pralat, Pawel |
| author_facet | Devroye, Luc Eide, Austin Pralat, Pawel |
| contents | Let $\mathcal{T}$ be a Galton-Watson tree with a given offspring distribution $ξ$, where $ξ$ is a $Z_{\geq 0}$-valued random variable with $E[ξ] = 1$ and $0 < σ^{2}:=Var[ξ] < \infty$. For $n \geq 1$, let $T_{n}$ be the tree $\mathcal{T}$ conditioned to have $n$ vertices. In this paper we investigate $b(T_n)$, the burning number of $T_n$. Our main result shows that asymptotically almost surely $b(T_n)$ is of the order of $n^{1/3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Burning Random Trees Devroye, Luc Eide, Austin Pralat, Pawel Combinatorics Probability Let $\mathcal{T}$ be a Galton-Watson tree with a given offspring distribution $ξ$, where $ξ$ is a $Z_{\geq 0}$-valued random variable with $E[ξ] = 1$ and $0 < σ^{2}:=Var[ξ] < \infty$. For $n \geq 1$, let $T_{n}$ be the tree $\mathcal{T}$ conditioned to have $n$ vertices. In this paper we investigate $b(T_n)$, the burning number of $T_n$. Our main result shows that asymptotically almost surely $b(T_n)$ is of the order of $n^{1/3}$. |
| title | Burning Random Trees |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2404.01545 |