Number theory, borderline dimension and extensive entropy in distributions of ranked data.

ABSTRACT: The consideration of an existing stochastic approach for the reproduction of ranked data pointed at a formal equivalence between its key mathematical expression and that for trajectories at the tangent bifurcation. This fact led to a nonlinear dynamical approach for rank distributions that shows similarities with universality classes in critical phenomena. The renormalization group (RG) fixed-point map f*(x) for a tangent bifurcation of arbitrary nonlinearity z > 1 has proved to be a powerful tool into which the formalism can be couched. The source distribution P(N) of the stochastic approach can be linked to f*(x) while the size-rank N(k) and frequency-rank F(k') distributions are obtained, respectively, from the map trajectories xt and the sums of its positions. We provide now an extensi

SUBMITTER: Velarde C 

PROVIDER: S-EPMC9794078 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature