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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 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 language | English |
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Article number | 87 |
Number of pages | 10 |
Journal | Electronic Communications in Probability |
Volume | 18 |
Early online date | 9 Nov 2013 |
DOIs | |
Publication status | Published - 2013 |
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Dive into the research topics of 'Increasing paths in regular trees'. Together they form a unique fingerprint.Projects
- 1 Finished
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EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts
Roberts, M. (PI)
Engineering and Physical Sciences Research Council
3/04/13 → 2/07/16
Project: Research council