Continuous-time random walk with a superheavy-tailed distribution of   waiting times
  We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is unbiased (biased) and the jump distribution has a finite second moment then the properly scaled probability density converges in the long-time limit to a symmetric two-sided (an asymmetric one-sided) exponential density. The convergence occurs in such a way that all the moments of the probability density grow slower than any power of time. As a consequence, the reference random walk can be viewed as a generic model of superslow diffusion. A few examples of superheavy-tailed distributions of waiting times that give rise to qualitatively different laws of superslow diffusion are considered. 
S. I. Denisov (1), H. Kantz (2) ((1) Sumy State University, Ukraine,   (2) Max Planck Institute for the Physics of Complex S...
cond-mat.stat-mech