2015/09/14 by Thomas Mountford, Mountford, Thomas, Daniel Valesin +1
Engineering · #Adhesion, Friction, and Surface Interactions #FOS: Mathematics #Gear and Bearing Dynamics Analysis #Lubricants and Their Additives #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1509.04339
openalex publication_date 2015/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the interface of the multitype contact process on ℤ. In this process, each site of ℤ is either empty or occupied by an individual of one of two species. Each individual dies with rate 1 and attempts to give birth with rate 2 R λ; the position for the possible new individual is chosen uniformly at random within distance R of the parent, and the birth is suppressed if this position is already occupied. We consider the process started from the configuration in which all sites to the left of the origin are occupied by one of the species and all sites to the right of the origin by the other species, and study the evolution of the region of interface between the two species. We prove that, under diffusive scaling, the position of the interface converges to Brownian motion.