Scaling transformation of random walk and generalized statistics

Fernando A Oliveira, Josivaldo A Cordeiro, Alaor S Chaves, Bernardo A Mello and Isaac M Xavier

Physica A: Statistical Mechanics and its Applications, 2001, vol. 295, issue 1, 201-208

Abstract: We use a decimation procedure in order to obtain the dynamical renormalization group transformation (RGT) properties of random walk distribution in a 1+1 lattice. We obtain an equation similar to the Chapman–Kolmogorov equation. First we show the existence of invariants of the RGT, and that the Tsallis distribution Rq(x)=[1+b(q−1)x2]1/(1−q) (q>1) is a quasi-invariant of the RGT. We obtain the map q′=f(q) from the RGT and show that this map has two fixed points: q=1, attractor, and q=2, repellor, which are the Gaussian and the Lorentzian, respectively. Finally we use those concepts to show that the nonadditivity of the Tsallis entropy needs to be reviewed.

Keywords: Scaling transformation; Random walks; Entropy (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:295:y:2001:i:1:p:201-208

DOI: 10.1016/S0378-4371(01)00074-7

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