Time evolution of correlations in a random sequential adsorption process

The pair correlation function C(r,t) for random sequential adsorption of particles with nearest-neighbor exclusion on a one-dimensional lattice evolves in time as C(r,t) = −1/2e−2(1−e−t)∑∞n=0{ [−2(1−e−t)]2n+r+1/(2n+r+1)!}. The distribution of the number of adsorbed particles on a lattice with N sites is shown to have a variance N(1 − e−t)e−4(1−e−t) for large N.