Scaling transformation of random walk and generalized statistics

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 R-q(x) = [1 + b(q - 1)x(2)](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. (C) 2001 Elsevier Science B.V. All rights reserved.