  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.
