Probability distribution function for the random sequential adsorption of hard-disks

The distribution of the number of hard-core objects deposited in a finite region through a random sequential adsorption process is analyzed. Three idealized model probability distributions for this problem are tested by comparing them with computer simulation distributions for the random sequential adsorption of hard-disks on a flat surface. A hypergeometric distribution where the effects of mutual exclusion between particles are incorporated by a coverage dependent effective volume per particle is shown to give best agreement with simulation results. This effective volume is derived in terms of the fluctuations in the particle number. Finite size effects in the fluctuations are taken into account.