Intrinsic complexity and scaling laws: From random fields to random vectors

Journal Article

© 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.

Full Text

Duke Authors

Cited Authors

  • Bryson, J; Zhao, H; Zhong, Y

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 17 / 1

Start / End Page

  • 460 - 481

Electronic International Standard Serial Number (EISSN)

  • 1540-3467

International Standard Serial Number (ISSN)

  • 1540-3459

Digital Object Identifier (DOI)

  • 10.1137/18M1187908

Citation Source

  • Scopus