Restricted random walk model as a new testing ground for the applicability of q-statistics
Makaleler > Tam Makale · 2011
Yazarlar: Uğur TIRNAKLI, H. J. JENSEN, C. TSALLIS
EPL (Europhysics Letters), SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2011, cilt 96, ss 40008-40008
DOI: 10.1209/0295-5075/96/40008
Özet
We present exact results obtained from Master Equations for the probability function P ( y , T ) of sums 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 * ∝ 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< p ≪1 is different from 1, although weak, but essential, deviation from the q -Gaussian does occur for a ≠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 ).