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Vertices of high degree in the preferential attachment tree

Brightwell, Graham 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

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Identification Number: 10.1214/EJP.v17-1803


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:
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: 20 Oct 2021 03:15

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