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

## 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 |
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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 |

Sets: | Departments > Mathematics |

Date Deposited: | 14 Mar 2012 16:46 |

Last Modified: | 20 Jan 2020 04:36 |

URI: | http://eprints.lse.ac.uk/id/eprint/42517 |

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