4.2 Article

Exponential decay of pairwise correlation in Gaussian graphical models with an equicorrelational one-dimensional connection pattern

Journal

STATISTICS & PROBABILITY LETTERS
Volume 171, Issue -, Pages -

Publisher

ELSEVIER
DOI: 10.1016/j.spl.2020.109016

Keywords

Gaussian graphical model; Multivariate normal distributions; Conditional independence graph; Equicorrelational one-dimensional connection pattern; Tridiagonal matrix; Gaussian free fields

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The study investigates a specific Gaussian graphical model and finds that pairwise correlation decays exponentially with distance, while also analyzing the difference between finite and infinite cases as the number of variables tends to infinity.
We consider a Gaussian graphical model associated with an equicorrelational and one-dimensional conditional independence graph. We show that pairwise correlation decays exponentially as a function of distance. We also provide a limit when the number of variables tend to infinity and quantify the difference between the finite and infinite cases. (C) 2020 Elsevier B.V. All rights reserved.

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