We consider a random spatial particle process with coagulation, a variant of the Marcus--Lushnikov process. We derive a formula for the joint distribution of all particle sizes at a given fixed time in terms of a Poisson-point process (via a Gibbs-measure) and use that to describe it in the limit of many particles in terms of a large-deviation principle. Based on an analysis of the rate function, we discuss criteria under which we can deduce a gelation phase transition (emergence of a particle with macroscopic size).

Joint work with Luisa Andreis (Milano), Heide Langhammer and Robert Patterson (Berlin).