Year: 2006
Type: article
Abstract: In this paper, random walks with independent steps distributed according to a Q-power-law probability distribution function with Q=1/(1-q) are studied. In the case q>1, we show that (i) a stochastic representation of the location of the walk after n steps can be explicitly given (for both finite and infinite variance) and (ii) a clear connection with the superstatistics framework can be established (including the anomalous diffusion case). In the case q<1, we prove that this random walk can be considered as the projection of an isotropic random walk, i.e., a random walk with fixed length steps and uniformly distributed directions. These results provide a natural extension of (i) the usual Gaussian framework and (ii) the infinite-covariance case of the superstatistics treatments.
Source: Physical Review E
Authors: C. Vignat, A. Plastino
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1977458183