Title: Renormalization group theory for percolation in time-varying networks,
Abstract: Motivated by multi-hop communication in unreliable wireless networks, we
present a percolation theory for time-varying networks. We develop a
renormalization group theory for a prototypical network on a regular grid,
where individual links switch stochastically between active and inactive
states. The question whether a given source node can communicate with a
destination node along paths of active links is equivalent to a percolation
problem. Our theory maps the temporal existence of multi-hop paths on an
effective two-state Markov process. We show analytically how this Markov
process converges towards a memory-less Bernoulli process as the hop distance
between source and destination node increases. Our work extends classical
percolation theory to the dynamic case and elucidates temporal correlations of
message losses. Quantification of temporal correlations has implications for
the design of wireless communication and control protocols, e.g. in
cyber-physical systems such as self-organized swarms of drones or smart traffic
networks.