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A dynamic network in a dynamic population: asymptotic properties

Britton, Tom; Lindholm, Mathias and Turova, Tatyana LU (2011) In Journal of Applied Probability 48(4). p.1163-1178
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 rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two... (More)
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 rho (of neighbouring nodes) which shows that rho 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Degree correlation, dynamic network, phase transition, random graph, stationary distribution
in
Journal of Applied Probability
volume
48
issue
4
pages
1163 - 1178
publisher
Applied Probability Trust
external identifiers
  • wos:000298938700018
  • scopus:84855295964
ISSN
1475-6072
DOI
10.1239/jap/1324046025
language
English
LU publication?
yes
id
af57bf22-ea28-4d91-83e3-d320c66be048 (old id 2348386)
date added to LUP
2012-02-24 12:30:42
date last changed
2017-01-01 03:07:38
@article{af57bf22-ea28-4d91-83e3-d320c66be048,
  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 rho (of neighbouring nodes) which shows that rho 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.},
  author       = {Britton, Tom and Lindholm, Mathias and Turova, Tatyana},
  issn         = {1475-6072},
  keyword      = {Degree correlation,dynamic network,phase transition,random graph,stationary distribution},
  language     = {eng},
  number       = {4},
  pages        = {1163--1178},
  publisher    = {Applied Probability Trust},
  series       = {Journal of Applied Probability},
  title        = {A dynamic network in a dynamic population: asymptotic properties},
  url          = {http://dx.doi.org/10.1239/jap/1324046025},
  volume       = {48},
  year         = {2011},
}