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Vertices of high degree in the preferential attachment tree


 
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1. Title Title of document Vertices of high degree in the preferential attachment tree
 
2. Creator Author's name, affiliation, country Graham Brightwell; London School of Economics; United Kingdom
 
2. Creator Author's name, affiliation, country Malwina Luczak; University of Sheffield; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random graphs; web graphs; concentration of measure; martingales; preferential attachment
 
3. Subject Subject classification 05C80; 60J10; 60G42
 
4. Description Abstract We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to its degree. We investigate the number $D_t(\ell)$ of vertices of each degree $\ell$ at each time $t$, focussing particularly on the case where $\ell$ is a growing function of $t$. We show that $D_t(\ell)$ is concentrated around its mean, which is approximately $4t/\ell^3$, for all $\ell \le (t/\log t)^{-1/3}$; this is best possible up to a logarithmic factor.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) EPSRC
 
7. Date (YYYY-MM-DD) 2012-02-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1803
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1803
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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