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Average shape of fluctuations for subdiffusive walks
Phys. Rev. E 69, 031104 – Published 22 March, 2004
DOI: https://doi.org/10.1103/PhysRevE.69.031104
Abstract
We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a fractional diffusion approach. We find that, in contrast with processes where the waiting time between increments has finite variance, the fluctuation shape is no longer a semicircle: it tends to adopt a tablelike form as the subdiffusive character of the process increases. The theoretical predictions are compared with numerical simulation results.
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