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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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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.
Library of Congress subject classification: H Social Sciences > H Social Sciences (General)
H Social Sciences > HA Statistics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 14 Mar 2012 16:46
URL: http://eprints.lse.ac.uk/42517/

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