WIAS Preprint No. 1364, (2008)

A stochastic fractal model of the universe related to the fractional Laplacian


  • Sabelfeld, Karl

2010 Mathematics Subject Classification

  • 65C05 65C20 76S05

2008 Physics and Astronomy Classification Scheme

  • 98.80.Jk, 95.75.Pq, 98.65.Dx


  • Stochastic fractals, fractal dimension of the Universe, fractional Laplace equation, boundary excitations, spectral and correlation functions


A new stochastic fractal model based on a fractional Laplace equation is developed. Exact representation for the spectral and correlation functions under random boundary excitation are obtained. Randomized spectral expansion is constructed for simulation of the solution of the fractional Laplace equation. We present calculations for 2D and 3D spaces for a series of fractional parameters showing a strong memory effect: the decay of correlations is several order of magnitudes less compared to the conventional Laplace equation model.

Appeared in

  • J. Cosmol. Astropart. Phys., 004 (2008) pp. 1475-7516.

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