Increasing paths in regular trees

M Roberts, Lee Zhuo Zhao

Research output: Contribution to journalArticlepeer-review

11 Citations (SciVal)
137 Downloads (Pure)


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 α=n/h is fixed and α>1/e, the probability that there exists such a path converges to 1 as h→∞. This complements a previously known result that the probability converges to 0 if α≤1/e.
Original languageEnglish
Article number87
Number of pages10
JournalElectronic Communications in Probability
Early online date9 Nov 2013
Publication statusPublished - 2013


Dive into the research topics of 'Increasing paths in regular trees'. Together they form a unique fingerprint.

Cite this