Density and correlation in a random sequential adsorption model

We consider a random sequential adsorption process on the one-dimensional lattice with nearest-neighbor exclusion. In this model, each site $s\in \mathbb{Z}$ starts empty and we will try to occupy it in time $t_s$, where $(t_s{)}_{s\in \mathbb{Z}}$ is a sequence of independent random variables uniformly distributed on the interval $[0,1]$. The site will be occupied if both of its neighbors are vacant. We provide a method to calculate the density of occupied sites up to the time $t$, as well as the pair correlation function.