Percolation and connection times in multi-scale dynamic networks

Christian Hirsch, Benedikt Jahnel and Elie Cali

Stochastic Processes and their Applications, 2022, vol. 151, issue C, 490-518

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.

Keywords: Continuum percolation; Multi-scale model; Scaling limit; Bounded-hop percolation; Wireless communication network (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:151:y:2022:i:c:p:490-518

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DOI: 10.1016/j.spa.2022.06.008

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