# Power-law random walks

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.
Type de document :
Article dans une revue
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2006, 74 (5), 〈10.1103/PhysRevE.74.051124〉
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693730
Contributeur : Christophe Vignat <>
Soumis le : mercredi 2 mai 2012 - 22:57:55
Dernière modification le : mercredi 11 avril 2018 - 12:12:03

### Citation

Christophe Vignat, A. Plastino. Power-law random walks. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2006, 74 (5), 〈10.1103/PhysRevE.74.051124〉. 〈hal-00693730〉

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