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arXiv · 1805.00194

Intrinsic Complexity And Scaling Laws: From Random Fields to Random Vectors

Jennifer Bryson·Hongkai Zhao·Yimin Zhong
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Abstract

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-Lo\'{e}ve 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, it becomes approximate embeddings of a set of random vectors. We provide a precise scaling law when the random vectors have independent and identically distributed entires using random matrix theory as well as when the random vectors has a specific covariance structure.

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Jennifer Bryson, Hongkai Zhao, Yimin Zhong. 2018-05-01. Intrinsic Complexity And Scaling Laws: From Random Fields to Random Vectors. https://arxiv.org/abs/1805.00194

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