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We consider Gaussian graphical models associated with an equicorrelationaland one-dimensional conditional independence graph. We show that pairwisecorrelation decays exponentially as a function of distance. We also provide alimit when the number of variables tend to infinity and quantify the differencebetween the finite and infinite cases.

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