An invariance principle for the edge of the branching exclusion process

We consider the one dimensional nearest neighbor branching exclusion process with initial configurations having a rightmost particle. We prove that, conveniently rescaled, the position of the rightmost particle (edge) converges to a nondegenerate Brownian motion. Convergence to a convex combination of measures concentrating on the full and empty configurations at the average position of the edge is established. A shape theorem for the process starting with a finite number of particles is also proven.