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Fractal percolation with neighbour interaction

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Fractals in Engineering
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Abstract

Fractal percolation was introduced by Benot Mandelbrot in [4] and further analysed in [1]. It can be considered as the most natural way to randomize the classical middle third Cantor set in a two-dimensional setting. Recently Peres [5] has discovered a close connection between fractal percolation and the path of Brownian motion.

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References

  1. Chayes, J.T., Chayes, L., Durrett, R. (1988): Connectivity properties of Mandelbrot’s percolation process. Probab. Theory Rel. Fields 77, 307–324.

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  4. Mandelbrot, B. (1974): Intermittent Turbulence in Self-similar Cascades: Divergence of High Moments and Dimension of the Carrier. J. Fluid Mech. 62, 331–358.

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  5. Peres, Y. (1996): Intersection-Equivalence of Brownian Paths and Certain Branching Processes. Comm. Math. Phys. 177, 417–434.

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  6. Siebesma, A.P., Tremblay, R.R., Erzan, A., Pietronero, L. (1989): Multifractal cascades with interactions. Physica A 156, no. 2, 613–627.

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© 1997 Springer-Verlag London Limited

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Burton, R.M., Coffey, T., Dekking, F.M., Hyman, K. (1997). Fractal percolation with neighbour interaction. In: Lévy Véhel, J., Lutton, E., Tricot, C. (eds) Fractals in Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0995-2_9

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  • DOI: https://doi.org/10.1007/978-1-4471-0995-2_9

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1253-2

  • Online ISBN: 978-1-4471-0995-2

  • eBook Packages: Springer Book Archive

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