On some stochastic coalescents

We consider infinite systems of macroscopic particles characterized by their masses. Each pair of particles with masses x and y coalesce at a given rate K(x, y). We assume that K satisfies a sort of Hölder property with index λ ∈ (0,1], and that the initial condition admits a moment of order λ. We show the existence of such infinite particle systems, as strong Markov processes enjoying a Feller property. We also show that the obtained processes are the only possible limits when making the number of particles tend to infinity in a sequence of finite particle systems with the same dynamics.