WIAS Preprint No. 2823, (2021)

Percolation and connection times in multi-scale dynamic networks


Authors

  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Hirsch, Christian
  • Cali, Eli

2020 Mathematics Subject Classification

  • 60K35 60F10 82C22

Keywords

  • Continuum percolation, multi-scale model, scaling limit, bounded-hop percolation, wireless communication network

DOI

10.20347/WIAS.PREPRINT.2823

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.

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