Monte Carlo analysis of the fluctuations in the random sequential adsorption of aligned and unaligned hard-squares

The fluctuations in the number of aligned and unaligned hard-squares deposited on a subvolume of a finite flat surface through a random sequential adsorption process are analyzed from Monte Carlo computer simulations. Approximate expressions for the coverage dependence of the relative fluctuation are obtained from a fit to simulation data. The influence of both the size of the subvolume and the size of the total adsorbing surface on the relative fluctuation is also examined. Two theoretical probability distributions, binomial and hypergeometric, are tested by comparing them with simulation distributions. A hypergeometric model where the effects of mutual exclusion between squares are incorporated by a coverage dependent effective volume per square is shown to give an excellent agreement with simulation distributions, even at coverages close to the jamming limit.