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

11/30/2020

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by   Guillaume Marrelec, et al.

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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.