Translator Disclaimer
2013 Increasing paths in regular trees
Matthew Roberts, Lee Zhao
Author Affiliations +
Electron. Commun. Probab. 18: 1-10 (2013). DOI: 10.1214/ECP.v18-2784

Abstract

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 $\alpha \leq 1/e$.

Citation

Download Citation

Matthew Roberts. Lee Zhao. "Increasing paths in regular trees." Electron. Commun. Probab. 18 1 - 10, 2013. https://doi.org/10.1214/ECP.v18-2784

Information

Accepted: 9 November 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1306.60128
MathSciNet: MR3141796
Digital Object Identifier: 10.1214/ECP.v18-2784

Subjects:
Primary: 60J80
Secondary: 60C05, 92D15

JOURNAL ARTICLE
10 PAGES


SHARE
Back to Top