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Shapes and sizes of arbitrary random walks at O(1/d3) II. Asphericity and prolateness parameters

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  • Wei, Gaoyuan
  • Zhu, Xuexian

Abstract

For arbitrary random walks in any d-dimensional space, expansions in powers of 1/d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed, which, at O(1/d3), yield very good approximations to exact values of the parameters for chains, rings, dumbbells and 3- and 5-arm regular stars. The 1/d-expansions have also been used to obtain an estimate of these shape asymmetry parameters for 3D Edwards chains, rings, dumbbells and 3-arm stars and to give a mathematical proof that infinitely large random nets such as Bethe lattice or starburst and Mckay's net exhibit spherical symmetry. For arbitrary random walks at d = ∞, it is proved that these parameters coincide with their corresponding factors, while for an end-looped self-avoiding walk, it is found that its shape asymmetry is even larger than that of an open SAW. An 1/f-expansion of the parameters for f-arm regular stars has also been obtained, and a comparison of the dimensionality dependence of the parameters with that of the corresponding factors has been made for the four types of random walks.

Suggested Citation

  • Wei, Gaoyuan & Zhu, Xuexian, 1997. "Shapes and sizes of arbitrary random walks at O(1/d3) II. Asphericity and prolateness parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 423-440.
    • Handle: RePEc:eee:phsmap:v:237:y:1997:i:3:p:423-440
    DOI: 10.1016/S0378-4371(96)00373-1
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    References listed on IDEAS

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    1. Michelsen Johannes, 1986. "Zielvorstellungen der Mitglieder landwirtschaftlicher Genossenschaften - Eine empirische Studie am Beispiel dänischer Genossenschaftsmolkereien," Zeitschrift für das gesamte Genossenschaftswesen, De Gruyter, vol. 36(1), pages 216-226, September.
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