Restricted random walk model as a new testing ground for the applicability of q-statistics

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Tirnakli U. , JENSEN H. J. , TSALLIS C.

EPL, vol.96, no.4, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 96 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.1209/0295-5075/96/40008
  • Title of Journal : EPL


We present exact results obtained from Master Equations for the probability function P(y, T) of sums y = Sigma(T)(t=1) x(t) of the positions x(t) of a discrete random walker restricted to the set of integers between -L and L. We study the asymptotic properties for large values of L and T. For a set of position-dependent transition probabilities the functional form of P(y, T) is with very high precision represented by q-Gaussians when T assumes a certain value T* proportional to L-2. The domain of y values for which the q-Gaussian apply diverges with L. The fit to a q-Gaussian remains of very high quality even when the exponent a of the transition probability g(x) = vertical bar x/L vertical bar(a) + p with 0 < p << 1 is different from 1, although weak, but essential, deviation from the q-Gaussian does occur for a not equal 1. To assess the role of correlations we compare the T dependence of P(y, T) for the restricted random walker case with the equivalent dependence for a sum y of uncorrelated variables x each distributed according to 1/g(x). Copyright (C) EPLA, 2011