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Percolation and connection times in multi-scale dynamic networks

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  • Hirsch, Christian
  • Jahnel, Benedikt
  • Cali, Elie

Abstract

We study the effects of mobility on two crucial characteristics in multi-scale dynamic networks: percolation and connection times. Our analysis provides insights into the question, to what extent long-time averages are well-approximated by the expected values of the corresponding quantities, i.e., the percolation and connection probabilities. In particular, we show that in multi-scale models, strong random effects may persist in the limit. Depending on the precise model choice, these may take the form of a spatial birth–death process or a Brownian motion. Despite the variety of structures that appear in the limit, we show that they can be tackled in a common framework with the potential to be applicable more generally in order to identify limits in dynamic spatial network models going beyond the examples considered in the present work.

Suggested Citation

  • Hirsch, Christian & Jahnel, Benedikt & Cali, Elie, 2022. "Percolation and connection times in multi-scale dynamic networks," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 490-518.
    • Handle: RePEc:eee:spapps:v:151:y:2022:i:c:p:490-518
    DOI: 10.1016/j.spa.2022.06.008
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    References listed on IDEAS

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    1. Hirsch, Christian & Jahnel, Benedikt & Cali, Elie, 2019. "Continuum percolation for Cox point processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3941-3966.
    2. Metzler, Ralf & Chechkin, Aleksei V. & Gonchar, Vsevolod Yu. & Klafter, Joseph, 2007. "Some fundamental aspects of Lévy flights," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 129-142.
    3. Dirk Erhard & Julián Martínez & Julien Poisat, 2017. "Brownian Paths Homogeneously Distributed in Space: Percolation Phase Transition and Uniqueness of the Unbounded Cluster," Journal of Theoretical Probability, Springer, vol. 30(3), pages 784-812, September.
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