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Two-point statistics of multifractal measures

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  • Meneveau, Charles
  • Chhabra, Ashvin B.

Abstract

The relationship between the ƒ(α) function of a multifractal and the spatial correlations of its singularity strengths is examined. An expression to compute the probability of observing two different singularities α’ and α″ within a distance r is derived for measures arising from isotropic random multiplicative processes. The correlation of α's is shown to decay logarithmically with distance. Possible applications to turbulence models are discussed, and the results are illustrated for a binomial measure, where the scaling of two-point correlation functions is shown to exhibit a phase transition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:164:y:1990:i:3:p:564-574
    DOI: 10.1016/0378-4371(90)90223-F
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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. 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.
    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. 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.

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