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- Title
DEGREES IN RANDOM SELF-SIMILAR BIPOLAR NETWORKS.
- Authors
CHEN CHEN; MAHMOUD, HOSAM
- 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.
- Subjects
SELF-similar processes; DISTRIBUTION (Probability theory); POLAR coordinates (Mathematics); MOMENT problems (Mathematics); MULTIVARIATE analysis; COVARIANCE matrices
- Publication
Journal of Applied Probability, 2016, Vol 53, Issue 2, p434
- ISSN
0021-9002
- Publication type
Article
- DOI
10.1017/jpr.2016.11