| Título: | Increasing paths in regular trees |
| Autores: |
Roberts, Matthew; University of Bath Zhao, Lee Zhuo; University of Cambridge |
| Fecha: | 2013-01-03 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
evolutionary biology; trees; branching processes; increasing paths 60J80 (primary); 60C05, 92D15 (secondary) |
| Descripción: | We consider a regular $n$-ary tree of height $h$, for which every vertex except the root is labelled with an independent and identically distributed continuous random variable. Taking motivation from a question in evolutionary biology, we consider the number of paths from the root to a leaf along vertices with increasing labels. We show that if $\alpha = n/h$ is fixed and $\alpha > 1/e$, the probability that there exists such a path converges to $1$ as $h \to \infty$. This complements a previously known result that the probability converges to $0$ if $\alpha \leq 1/e$. |
| Idioma: | Inglés |
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