Recursive approach to random sequential adsorption

We present a generalization of Renyi's [A. Renyi, Trans. Math. Stat. Prob. 4, 205 (1963)] classical solution to the one-dimensional random sequential adsorption (RSA) problem, to the case where particle sizes are drawn from an arbitrary distribution, a process known as competitive RSA. We formulate the process using recursive relations, and without explicitly solving the equations, we extract limiting behavior which leads to exact analytic expressions for the final coverage. Our analysis is confirmed by computer simulations.