On The Complexity Of Statistical Models Admitting Correlations

Abstract

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.

15 pages, no figures; improved version

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• Information Geometry of Quantum Entangled Gaussian Wave-Packets
• Theoretical investigations of an information geometric approach to complexity
• Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference