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

Abstract

We consider Gaussian graphical models 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.

Paper accepted for publication in Statistics and Probability Letters