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DY: Fachverband Dynamik und Statistische Physik

DY 51: Networks: From Topology to Dynamics (joint session DY/SOE)

DY 51.2: Vortrag

Mittwoch, 14. März 2018, 15:45–16:00, MA 001

Renormalisation group theory for percolation in time-varying networks — •Jens Karschau, Marco Zimmerling, and Benjamin M. Friedrich — cfaed | TU Dresden, Dresden, Germany

Wireless communication networks require reliable routing of messages, despite the fact that individual networks links are unreliable. Multi-hop routing protocols propose a promising solution to overcome the issue of message loss. For these protocols, successful relay of a message defines a percolation problem.

Here, we present a percolation theory for a minimal model, where individual links switch between an active and an inactive state according to a two-state Markov process. Using renormalization group theory, we analytically compute the complete statistics of failure events. We show how the time-dependent probability to find a path of active links between two designated nodes converges towards an effective Bernoulli process, i.e. without memory, as the hop distance between the nodes increases. Our work extends classical percolation theory to the dynamic case. It elucidates temporal correlations of message losses with implications for the design of communication protocols and control algorithms.

Reference: arXiv:1708.05704