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Abstract
We consider a regular nary 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 

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

EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts
Engineering and Physical Sciences Research Council
3/04/13 → 2/07/16
Project: Research council