Abstract
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 asx α−1 atx
1 with the lengthx of the filling interval. We develop a scaling theory describing such mixture-deposition processes and show that the scaled hole-size distributionΦ(ξ), with ξ=xt z a scaling variable, decays with the scaled mass ξ as ξ−θexp(—const·ξ1+α) as ξ→∞. We determine scaling exponentsz andθ, and find that at large times the coverageθ(t) has a power-law form 1 − θ(t)≃t −v with nonuniversal exponent ν=(2−θ)/(1+α) depending on the homogeneity index α.
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Krapivsky, P.L. Kinetics of random sequential parking on a line. J Stat Phys 69, 135–150 (1992). https://doi.org/10.1007/BF01053786
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DOI: https://doi.org/10.1007/BF01053786