Continuous-time random walk theory of superslow diffusion

Author： Denisov S. I.   Kantz H.  

Publisher： Edp Sciences

E-ISSN： 1286-4854|92|3|30001-30001

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.92, Iss.3, 2010-11, pp. : 30001-30001

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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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