In the Lévy walk model of the infinite-horizon Lorentz gas, the authors derive a mixed Gaussian central limit theorem with width set by ln t + 2ζ and an infinite-density tail that fixes all higher moments and half the variance.
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Refined central limit theorem and infinite density tail of the Lorentz gas from Levy walk
In the Lévy walk model of the infinite-horizon Lorentz gas, the authors derive a mixed Gaussian central limit theorem with width set by ln t + 2ζ and an infinite-density tail that fixes all higher moments and half the variance.