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Average shape of fluctuations for subdiffusive walks

Santos B. Yuste·L. Acedo
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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 table-like form as the subdiffusive character of the process increases. The theoretical predictions are compared with numerical simulation results.

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Santos B. Yuste, L. Acedo. 2004-02-19. Average shape of fluctuations for subdiffusive walks. https://doi.org/10.1103/physreve.69.031104

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