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

Guillaume Marrelec (1) , Alain Giron (1) , Laura Messio (2)

1 LIB - Laboratoire d'Imagerie Biomédicale [Paris]
2 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

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.

Mots clés: Gaussian graphical model; multivariate normal distributions; conditional independence graph; equicorrelational one-dimensional connection pattern; tridiagonal matrix; circulant matrix; Gaussian free fields

Domaines: Statistiques [stat]; Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]

Guillaume Marrelec, Alain Giron, Laura Messio. Exponential decay of pairwise correlation in Gaussian graphical models with an equicorrelational one-dimensional connection pattern. Statistics and Probability Letters, 2021, pp.109016. ⟨10.1016/j.spl.2020.109016⟩. ⟨hal-03061276⟩