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Two classes of interacting particle systems on $\mathbb{Z}$ are shown to bePfaffian point processes at fixed times, and for all deterministic initialconditions. The first comprises coalescing and branching random walks, thesecond annihilating random walks with pairwise immigration. Various limitingPfaffian point processes on $\mathbb{R}$ are found by diffusive rescaling,including the point set process for the Brownian net.

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Examples of interacting particle systems on $\mathbb{Z}$ as Pfaffian  point processes: coalescing branching random walks and annihilating random  walks with immigration