We consider a class of interacting particle systems with values in $[0,∞)^{mathbb{Z}^d}$, of which the binary contact path process is an example. For $d geq 3$ and under a certain square integrability condition on the total number of the particles, we prove a central limit theorem for the density of the particles, together with upper bounds for the density of the most populated site and the replica overlap.
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