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Increasing paths in regular trees


 
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1. Title Title of document Increasing paths in regular trees
 
2. Creator Author's name, affiliation, country Matthew Roberts; University of Bath; United Kingdom
 
2. Creator Author's name, affiliation, country Lee Zhuo Zhao; University of Cambridge; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) evolutionary biology; trees; branching processes; increasing paths
 
3. Subject Subject classification 60J80 (primary); 60C05, 92D15 (secondary)
 
4. Description 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 $\alpha \leq 1/e$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) EPSRC grant EP/K007440/1, EP/I03372X/1, ESF, Oberwolfach Leibniz Graduate Student programme
 
7. Date (YYYY-MM-DD) 2013-11-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2784
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2784
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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