A particle system with cooperative branching and coalescence

@article{Sturm2013APS,
  title={A particle system with cooperative branching and coalescence},
  author={Anja Sturm and Jan M. Swart},
  journal={arXiv: Probability},
  year={2013}
}
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the particle present on that site ("coalescence"). We show that the system undergoes a phase transition as the branching rate is increased. For small branching rates, the upper invariant law is trivial, and the process started with finitely many particles a.s… 

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