Almost sure exponential convergence to consensus of random gossip algorithms


Correspondence to: Giorgio Picci, Department of Information Engineering, University of Padova, via Gradenigo 6/B, 35131 Padova, Italy.



In this paper, we provide a proof of almost sure exponential convergence to consensus for a general class of ergodic edge selection processes. The proof is based on the multiplicative ergodic theorem of Oseledec and also applies to continuous time gossip algorithms. An example of exponential convergence in a non ergodic case is also discussed. Copyright © 2012 John Wiley & Sons, Ltd.