Average shape of fluctuations for subdiffusive walks

Details Average shape of fluctuations for subdiffusive walks Average shape of fluctuations for subdiffusive walks

2003-10-21

arxiv.org/abs/cond-mat/0310491v2

Phys. Rev. E 69, 031104 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 6 figures. Accepted for publication Phys. Rev. E (Replaced for the latest version, in press.) Section II rewritten

Scientific paper

10.1103/PhysRevE.69.031104

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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