  We consider open multi-agent systems. Unlike the systems usually studied in
the literature, here agents may join or leave while the process studied takes
place. The system composition and size evolve thus with time. We focus here on
systems where the interactions between agents lead to pairwise gossip averages,
and where agents either arrive or are replaced at random times. These events
prevent any convergence of the system. Instead, we describe the expected system
behavior by showing that the evolution of scaled moments of the state can be
characterized by a 2-dimensional (possibly time-varying) linear dynamical
system. We apply this technique to two cases : (i) systems with fixed size
where leaving agents are immediately replaced, and (ii) systems where new
agents keep arriving without ever leaving, and whose size grows thus unbounded.
