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We present an analytical computation of the asymptotic temporal behavior ofthe information geometric complexity (IGC) of finite-dimensional Gaussianstatistical manifolds in the presence of microcorrelations (correlationsbetween microvariables). We observe a power law decay of the IGC at a ratedetermined by the correlation coefficient. It is found that microcorrelationslead to the emergence of an asymptotic information geometric compression of thestatistical macrostates explored by the system at a faster rate than thatobserved in absence of microcorrelations. This finding uncovers an importantconnection between (micro)-correlations and (macro)-complexity in Gaussianstatistical dynamical systems.

The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models