Examples of interacting particle systems on $\mathbb{Z}$ as Pfaffian   point processes: coalescing branching random walks and annihilating random   walks with immigration
  Two classes of interacting particle systems on $\mathbb{Z}$ are shown to be Pfaffian point processes at fixed times, and for all deterministic initial conditions. The first comprises coalescing and branching random walks, the second annihilating random walks with pairwise immigration. Various limiting Pfaffian point processes on $\mathbb{R}$ are found by diffusive rescaling, including the point set process for the Brownian net. 
Barnaby Garrod, Roger Tribe, Oleg Zaboronski
math.PR