×

zbMATH — the first resource for mathematics

Multilayer parking with screening on a random tree. (English) Zbl 1191.82030
Summary: We present a multilayer particle-deposition model on a random tree. We derive the time-dependent densities of the first and second layer analytically and show that for all trees the limiting density of the first layer exceeds the density in the second layer. We also provide a procedure to calculate higher-layer densities and prove that random trees have a higher limiting density in the first layer than regular trees. Finally, we compare densities between the first and second layer and between regular and random trees.

MSC:
82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
90B20 Traffic problems in operations research
05C80 Random graphs (graph-theoretic aspects)
PDF BibTeX Cite
Full Text: DOI arXiv
References:
[1] Meakin, P.: Diffusion-controlled deposition on fibers and surfaces. Phys. Rev. A 27(5), 1616–1623 (1983)
[2] Dehling, H.G., Fleurke, S.R.: The sequential frequency assignment process. In: Proc. of the 12th WSEAS Internat. Conf. on Appl. Math., pp. 280–285, Cairo, Egypt (2007)
[3] Fleurke, S.R., Külske, C.: A second-row parking paradox. J. Stat. Phys. 136(2), 285–295 (2009) · Zbl 1180.82039
[4] Dehling, H.G., Fleurke, S.R., Külske, C.: Parking on a random tree. J. Stat. Phys. 133(1), 151–157 (2008) · Zbl 1151.82390
[5] Gouet, R., Sudbury, A.: Blocking and dimer processes on the Cayley tree. J. Stat. Phys. 130, 935–955 (2008) · Zbl 1214.82069
[6] Sudbury, A.: Random sequential adsorption on random trees. J. Stat. Phys. 136(1), 51–58 (2009) · Zbl 1173.82024
[7] Liggett, T.M.: Interacting Particle Systems. Springer, New York (1985) · Zbl 0559.60078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.