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Degrees in random self-similar bipolar networks

Part of: Operations research and management science Limit theorems Combinatorial probability

Published online by Cambridge University Press:  21 June 2016

Chen Chen  and
Hosam Mahmoud
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.
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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.

Keywords

Random structurenetworkself-similarityrandom graphdegreestochastic recurrencePólya urnmultivariate normal distribution

MSC classification

Primary: 90B15: Network models, stochastic
Secondary: 60C05: Combinatorial probability 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 434 - 447
Copyright
Copyright © Applied Probability Trust 2016 

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