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Degrees in random self-similar bipolar networks

Published online by Cambridge University Press:  21 June 2016

Chen Chen*
Affiliation:
The George Washington University
Hosam Mahmoud*
Affiliation:
The George Washington University
*
* Postal address: Department of Statistics, The George Washington University, 801 22nd St. NW, Washington, DC 20052, USA.
* Postal address: Department of Statistics, The George Washington University, 801 22nd St. NW, Washington, DC 20052, USA.

Abstract

We investigate several aspects of a self-similar evolutionary process that builds a random bipolar network from building blocks that are themselves small bipolar networks. We characterize admissible outdegrees in the history of the evolution. We obtain the limit distribution of the polar degrees (when suitably scaled) characterized by its sequence of moments. We also obtain the asymptotic joint multivariate normal distribution of the number of nodes of small admissible outdegrees. Five possible substructures arise, and each has its own parameters (mean vector and covariance matrix) in the multivariate distribution. Several results are obtained by mapping bipolar networks into Pólya urns.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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