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Some results on multifractal correlations

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  • Lee, Sung Jong
  • Halsey, Thomas C.

Abstract

We have performed a numerical and analytical study of multifractal correlations in a two-scale random Cantor set. At large distances, for |α - ”’| not very large, we find qualitative agreement between canonical simulation results (also counting results) and the formula recently proposed by Meneveau and Chhabra, following work of Cates and Deutsch. For |α - α’| large, a new correlation scaling function ƒ̃(α, α’, ω) which is linear in log(r) is obtained due to a transition of the moment-scaling function from Cates and Deutsch behavior to a differing behavior for some part of its domain. This linear ƒ̃(α, α’, ω) is consistent with numerical results.

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  • Lee, Sung Jong & Halsey, Thomas C., 1990. "Some results on multifractal correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 164(3), pages 575-592.
    • Handle: RePEc:eee:phsmap:v:164:y:1990:i:3:p:575-592
    DOI: 10.1016/0378-4371(90)90224-G
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    References listed on IDEAS

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    1. Deutsch, Joseph & Hakim, Simon & Weinblatt, J., 1987. "A micro model of the criminal's location choice," Journal of Urban Economics, Elsevier, vol. 22(2), pages 198-208, September.
    2. Meneveau, Charles & Chhabra, Ashvin B., 1990. "Two-point statistics of multifractal measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 164(3), pages 564-574.
    3. Pietronero, L. & Erzan, A. & Evertsz, C., 1988. "Theory of Laplacian fractals: Diffusion limited aggregation and dielectric breakdown model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 151(2), pages 207-245.
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    1. Meneveau, Charles & Chhabra, Ashvin B., 1990. "Two-point statistics of multifractal measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 164(3), pages 564-574.

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