Non-Gaussian random walks

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Abstract
The authors present an explicit expression for the probability distribution for the position of a continuous-time random walker in an arbitrary number of dimensions when the interjump density has a long time tail, in contrast to earlier results which require numerical inversion of a Fourier integral. They replace this numerical procedure by one that relies on the method of steepest descents. Their results are applied to diffusion on a comb and on a percolation cluster generated on a Cayley tree at criticality and are confirmed numerically.

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