Vertices of high degree in the preferential attachment tree
Dublin Core | PKP Metadata Items | Metadata for this Document | |
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 | |
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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