Exponential decay of pairwise correlation in Gaussian graphical models with an equicorrelational one-dimensional connection pattern
Statistics Theory
2021-06-22 v1 Statistical Mechanics
Mathematical Physics
math.MP
Statistics Theory
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.
Cite
@article{arxiv.2011.14614,
title = {Exponential decay of pairwise correlation in Gaussian graphical models with an equicorrelational one-dimensional connection pattern},
author = {Guillaume Marrelec and Alain Giron and Laura Messio},
journal= {arXiv preprint arXiv:2011.14614},
year = {2021}
}
Comments
Paper accepted for publication in Statistics and Probability Letters