Translator Disclaimer
December 2011 A dynamic network in a dynamic population: asymptotic properties
Tom Britton, Mathias Lindholm, Tatyana Turova
Author Affiliations +
J. Appl. Probab. 48(4): 1163-1178 (December 2011). DOI: 10.1239/jap/1324046025


We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation ρ (of neighbouring nodes) which shows that ρ is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters.


Download Citation

Tom Britton. Mathias Lindholm. Tatyana Turova. "A dynamic network in a dynamic population: asymptotic properties." J. Appl. Probab. 48 (4) 1163 - 1178, December 2011.


Published: December 2011
First available in Project Euclid: 16 December 2011

zbMATH: 1231.92054
MathSciNet: MR2896674
Digital Object Identifier: 10.1239/jap/1324046025

Primary: 92D30
Secondary: 60J80

Keywords: degree correlation , dynamic network , phase transition , random graph , stationary distribution

Rights: Copyright © 2011 Applied Probability Trust


This article is only available to subscribers.
It is not available for individual sale.

Vol.48 • No. 4 • December 2011
Back to Top