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

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

2011-05-31

arxiv.org/abs/1105.6184v2

Physics

Condensed Matter

Statistical Mechanics

5 pages, 7 figs, EPL (2011), in press

Scientific paper

We present exact results obtained from Master Equations for the probability function P(y,T) of sums $y=\sum_{t=1}^T x_t$ 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 $T^*\propto L^2$. 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)=|x/L|^a+p with 0

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