Journal of Statistical Physics

, Volume 171, Issue 3, pp 434–448 | Cite as

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

  • Pierre Nazé


Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel–Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag–Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.


Weakly chaotic dynamics Deterministic subdiffusion Copula modeling 



I thank Marcus V. S. Bonança, Alberto Saa and Roberto Venegeroles for reading the manuscript; A. Suzuki and M. L. Viola for discussions about copula modeling. This work was financed by CNPq and CAPES.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Unicamp, Instituto de Física “Gleb Wataghin”, DFCMCampinasBrazil

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