KINETICS OF RANDOM SEQUENTIAL PARKING ON A LINE

We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the known car-parking problem and we present an alternate solution to this problem. We also consider the general homogeneous case when the parking distribution varies as x(alpha-1) at x much less than 1 with the length x of the filling interval. We develop a scaling theory describing such mixture-deposition processes and show that the scaled hole-size distribution PHI(xi), with xi = xt(z) a scaling variable, decays with the scaled mass xi as xi(-theta) exp(- const . xi(1+alpha) as xi --> infinity. We determine scaling exponents z and theta, and find that at large times the coverage theta(t) has a power-law form 1 - theta(t) congruent-to t(-nu) with nonuniversal exponent nu = (2 - theta)/(1 + alpha) depending on the homogeneity index alpha.