Continuous-time random walk with a superheavy-tailed distribution of waiting times

Details Continuous-time random walk with a superheavy-tailed distribution of waiting times Continuous-time random walk with a superheavy-tailed distribution of waiting times

2011-02-13

arxiv.org/abs/1102.2590v2

Phys. Rev. E 83, 041132 (2011)

Physics

Condensed Matter

Statistical Mechanics

7 pages

Scientific paper

10.1103/PhysRevE.83.041132

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.

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