title: Continuous-time random walk with a superheavy-tailed distribution of waiting times.
abstract: 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.
authors: Sumy State University, Rimsky-Korsakov Street 2, UA-40007 Sumy, Ukraine. denisov@sumdu.edu.ua
authors: S I
authors: SI
authors: Denisov
authors: H
authors: H
authors: Kantz