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arXiv · 1010.0782

Continuous-time random walk theory of superslow diffusion

S. I. Denisov·H. Kantz
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Abstract

Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this behavior of the variance occurs when the complementary cumulative distribution function of waiting times is asymptotically described by a slowly varying function. In this case, we derive a general representation of the laws of superslow diffusion for both biased and unbiased versions of the model and, to illustrate the obtained results, consider two particular classes of waiting-time distributions.

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BibTeXRIS

S. I. Denisov, H. Kantz. 2010-10-05. Continuous-time random walk theory of superslow diffusion. https://doi.org/10.1209/0295-5075%2F92%2F30001

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