On The Complexity Of Statistical Models Admitting Correlations

Details On The Complexity Of Statistical Models Admitting Correlations On The Complexity Of Statistical Models Admitting Correlations

2009-05-18

arxiv.org/abs/0905.2907v2

Phys. Scr. 82, 035007 (2010)

Physics

Mathematical Physics

15 pages, no figures; improved version

Scientific paper

We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the system. The algorithmic structure of our asymptotic computations is presented and special focus is devoted to the diagonalization procedure that allows to simplify the problem in a remarkable way. We observe a power law decay of the information geometric complexity at a rate determined by the correlation coefficient. We conclude that macro-correlations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored on the configuration manifold of the model in its evolution between the initial and final macrostates.

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