A solvable model for irreversible adsorption of large particles

In this paper we propose and solve analytically a class of models generalizing the ballistic deposition (BD) model for irreversible adsorption of hard particles onto a line. In these new models, when an incoming particle interacts with an adsorbed one, it adsorbs next to it leaving between them a small gap of random size with characteristic length λ. The first moments of the gap distribution suffice to describe the lowest-order corrections to the BD model. In particular, for small values of λ we obtain an asymptotic approach to the BD jamming coverage in agreement with previous Brownian simulations which take into account diffusion and gravity.