Intrinsic complexity and scaling laws: From random fields to random vectors
© 2019 Society for Industrial and Applied Mathematics. Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g., the covariance function, based on the Karhumen Loeve expansion. We then show scaling laws for the intrinsic complexity of a random field in terms of the correlation length as it goes to 0. In the discrete setting, the analogy is approximation of a set of random vectors based on principal component analysis. We provide a precise scaling law when the random vectors have independent and identically distributed entries using random matrix theory as well as when the random vectors have a specific covariance structure.
Bryson, J; Zhao, H; Zhong, Y
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