Some asymptotic estimates in the random parking problem

Abstract

As shown by exact calculations in one dimension (d=1) and by computer experiments for d=2, the density of the jammed state in the random parking problem tends to its limit value as y_d( infinity )-a_d tau ^-1d/, where tau is the time and y_d( infinity ) the final density. The pair correlation function diverges at contact in the final state. Both properties are due to the sure filling of small holes.