Agreement over noisy networks

The authors consider the agreement problem over noisy communication networks. This problem is analysed via a blend of ideas from stochastic stability (supermartingales) and algebraic graph theory (spectra of graph Laplacians). In this venue, the authors show that the noisy agreement protocol has a guaranteed probabilistic convergence, provided that an embedded step size meets a graph theoretic constraint. The authors then proceed to define a pertinent graph parameter and point out the ramifications of having noisy information exchange links in networks that can be modelled as random and random geometric graphs.