Brightwell, Graham 
ORCID: 0000-0001-5955-3628 and Luczak, Malwina J.
(2012)
Vertices of high degree in the preferential attachment tree.
Electronic Journal of Probability, 17.
pp. 1-43.
ISSN 1083-6489
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(l) of vertices of each degree l at each time t, focussing particularly on the case where l is a growing function of t. We show that D t(l) is concentrated around its mean, which is approximately 4t=l 3, for all l ≤ (t= log t) -1/3; this is best possible up to a logarithmic factor.
| Item Type: | Article |
|---|---|
| Official URL: | http://ejp.ejpecp.org/index// |
| Additional Information: | © 2012 The Authors. |
| Divisions: | Mathematics |
| Subjects: | H Social Sciences > H Social Sciences (General) H Social Sciences > HA Statistics |
| Date Deposited: | 14 Mar 2012 16:46 |
| Last Modified: | 14 Dec 2025 07:15 |
| URI: | http://eprints.lse.ac.uk/id/eprint/42517 |
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