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.
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Submitted on : Wednesday, May 2, 2012 - 10:57:55 PM
Last modification on : Wednesday, April 11, 2018 - 12:12:03 PM

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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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