Asynchronous peer-to-peer consensus in varieties.

Summary The objective of this paper is to propose a generalization of the asynchronous distributed peer-to-peer consensus algorithm of \cite{boyd:gossip} for data belonging to a Riemmannian variety. We show its convergence in the case where the variety is simply connected and without focal points. The interest of this algorithm is illustrated in the case where a network of sensors seeks to find a consensus on discrete probability laws. However, the field of applications covered by this algorithm goes far beyond this framework.