Power-law random walks - Archive ouverte HAL Access content directly
Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2006

Power-law random walks


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.

Dates and versions

hal-00693730 , version 1 (02-05-2012)



Christophe Vignat, A. Plastino. Power-law random walks. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2006, 74 (5), ⟨10.1103/PhysRevE.74.051124⟩. ⟨hal-00693730⟩
190 View
0 Download



Gmail Mastodon Facebook X LinkedIn More