Random deposition model with a constant capture length

We introduce a sequential model for the deposition and aggregation of particles in the submonolayer regime. Once a particle has been randomly deposited on the substrate, it sticks to the closest atom or island within a distance l, otherwise it sticks to the deposition site. We study this model both numerically and analytically in one dimension. A clear comprehension of its statistical properties is provided, thanks to capture equations and to the analysis of the island-island distance distribution.