We consider coagulation equations of Smoluchowski or Flory type where the
total merge rate has a bilinear form π(y)⋅Aπ(x) for a vector of
conserved quantities π, generalising the multiplicative kernel. For these
kernels, a gelation transition occurs at a finite time tg∈(0,∞), which can be given exactly in terms of an eigenvalue problem in
finite dimensions. We prove a hydrodynamic limit for a stochastic coagulant,
including a corresponding phase transition for the largest particle, and
exploit a coupling to random graphs to extend analysis of the limiting process
beyond the gelation time.Comment: Generalises the previous version to focus on general coagulation
processes of bilinear type, without restricting to the single example of the
previous version. The previous results are mentioned as motivation, and all
results of the previous version can be obtained from this more general
versio