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

Abstract

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.

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Tom Britton. Mathias Lindholm. Tatyana Turova. "A dynamic network in a dynamic population: asymptotic properties." J. Appl. Probab. 48 (4) 1163 - 1178, December 2011. https://doi.org/10.1239/jap/1324046025

Information

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

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

Subjects:
Primary: 92D30
Secondary: 60J80

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

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 4 • December 2011
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