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Scaling transformation of random walk and generalized statistics

Author

Listed:
  • Oliveira, Fernando A
  • Cordeiro, Josivaldo A
  • Chaves, Alaor S
  • Mello, Bernardo A
  • Xavier, Isaac M

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.

Suggested Citation

  • Oliveira, Fernando A & Cordeiro, Josivaldo A & Chaves, Alaor S & Mello, Bernardo A & Xavier, Isaac M, 2001. "Scaling transformation of random walk and generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 201-208.
    • Handle: RePEc:eee:phsmap:v:295:y:2001:i:1:p:201-208
    DOI: 10.1016/S0378-4371(01)00074-7
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