Exponential Decay Of Pairwise Correlation In Gaussian Graphical Models With An Equicorrelational One-Dimensional Connection Pattern

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.