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

Published online by Cambridge University Press:  24 March 2016

Gennady Samorodnitsky ,
Sidney Resnick ,
Don Towsley ,
Richard Davis ,
Amy Willis  and
Phyllis Wan
Gennady Samorodnitsky
Affiliation:
School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: gs18@cornell.edu
Sidney Resnick*
Affiliation:
School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA.
Don Towsley
Affiliation:
Department of Computer Science, University of Massachusetts, Amherst, MA 01003, USA. Email address: towsley@cs.umass.edu
Richard Davis
Affiliation:
Department of Statistics, Columbia University, New York, NY 10027, USA. Email address: rdavis@stat.columbia.edu
Amy Willis
Affiliation:
Department of Statistical Science, Cornell University, Ithaca, NY 14853, USA. Email address: adw96@cornell.edu
Phyllis Wan
Affiliation:
Department of Statistics, Columbia University, New York, NY 10027, USA. Email address: phyllis@stat.columbia.edu
*
*** Email address: sir1@cornell.edu
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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 in-degree 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.

Keywords

Multivariate heavy tailspreferential attachment modelscale-free networks
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 146 - 161
Copyright
Copyright © Applied Probability Trust 2016 

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References

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