Degrees in random self-similar bipolar networks. (21st June 2016)

• Record Type: Journal Article
• Authors: Chen, Chen; Mahmoud, Hosam
• Is Part Of: Journal of applied probability. Volume 53:Number 2(2016)
• Page Start: 434
• Page End: 447
• Publication Date: 2016-06-21
• Subjects: Random structure, -- network, -- self-similarity, -- random graph, -- degree, -- stochastic recurrence, -- Pólya urn, -- multivariate normal distribution; Primary 05082, -- 90B15, -- Secondary 60C05, -- 60F05; 519.2
• DOI: 10.1017/jpr.2016.11
• Languages: English
• ISSNs: 0021-9002

Abstract

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.