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.

Automated summary

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.