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.

中文翻译：

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具有等相关一维连接模式的高斯图形模型中成对相关的指数衰减

我们考虑与等相关和一维条件独立图相关联的高斯图模型。我们表明，成对相关性作为距离的函数呈指数衰减。当变量的数量趋于无穷大时，我们还提供了一个限制，并量化了有限和无限情况之间的差异。