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2012 Vertices of high degree in the preferential attachment tree
Graham Brightwell, Malwina Luczak
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Electron. J. Probab. 17: 1-43 (2012). DOI: 10.1214/EJP.v17-1803

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.

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Graham Brightwell. Malwina Luczak. "Vertices of high degree in the preferential attachment tree." Electron. J. Probab. 17 1 - 43, 2012. https://doi.org/10.1214/EJP.v17-1803

Information

Accepted: 11 February 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.05197
MathSciNet: MR2892327
Digital Object Identifier: 10.1214/EJP.v17-1803

Subjects:
Primary: 05C80
Secondary: 60G42, 60J10

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Vol.17 • 2012
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