Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site

Abstract

We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also derive a limiting estimate and an exponential estimate on the fluctuations of the position of the rightmost particle.

17 pages; a short section devoted to numerical simulations is added; other small changes and improvements

References in corpus (4)

• Minima in branching random walks
• Spatial birth and death processes as solutions of stochastic equations
• Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes
• Spatial growth processes with long range dispersion: microscopics, mesoscopics, and discrepancy in spread rate