Continuous-time random walk theory of superslow diffusion
Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Straße 38, D-01187 Dresden, Germany, EU
2 Sumy State University - Rimsky-Korsakov Street 2, UA-40007 Sumy, Ukraine
Accepted: 13 October 2010
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.
PACS: 05.40.Fb – Random walks and Levy flights / 02.50.Ey – Stochastic processes
© EPLA, 2010