An invariance principle for the edge of the branching exclusion process

C. Cammarota and P. A. Ferrari

Stochastic Processes and their Applications, 1991, vol. 38, issue 1, 1-11

Abstract: 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.

Keywords: branching; exclusion; process; invariance; principle; edge; process (search for similar items in EconPapers)
Date: 1991
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