Fig. 1.
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Two-point correlation function for the 1D Rayleigh-Levy flights (before smoothing). The predictions are for ℓ0 = 1. The solid lines are the exact shapes derived from Eq. (5) exhibiting a clear exclusion zone for r < ℓ0. The dashed is the large scale asymptotic form. it can be observed that the exact solution converges very rapidly to the asymptotic form.
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