Nonstandard regular variation of in-degree and out-degree in the preferential attachment model

Gennady Samorodnitsky, Sidney Resnick, Don Towsley, Richard Davis, Amy Willis, Phyllis Wan

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

For the directed edge preferential attachment network growth model studied by Bollobás et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of indegree and out-degree has jointly regularly varying tails. Typically, the marginal tails of the in-degree distribution and the out-degree distribution have different regular variation indices and so the joint regular variation is nonstandard. Only marginal regular variation has been previously established for this distribution in the cases where the marginal tail indices are different.

Original languageEnglish (US)
Pages (from-to)146-161
Number of pages16
JournalJournal of Applied Probability
Volume53
Issue number1
DOIs
StatePublished - Mar 1 2016

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Regular Variation
Preferential Attachment
Degree Distribution
Tail
Tail Index
Growth Model
Joint Distribution
Network Model
Model
Regular variation

Keywords

  • Multivariate heavy tails
  • Preferential attachment model
  • Scale-free network

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Cite this

Nonstandard regular variation of in-degree and out-degree in the preferential attachment model. / Samorodnitsky, Gennady; Resnick, Sidney; Towsley, Don; Davis, Richard; Willis, Amy; Wan, Phyllis.

In: Journal of Applied Probability, Vol. 53, No. 1, 01.03.2016, p. 146-161.

Research output: Contribution to journalArticle

Samorodnitsky, Gennady ; Resnick, Sidney ; Towsley, Don ; Davis, Richard ; Willis, Amy ; Wan, Phyllis. / Nonstandard regular variation of in-degree and out-degree in the preferential attachment model. In: Journal of Applied Probability. 2016 ; Vol. 53, No. 1. pp. 146-161.
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