Selfadhesivity is a property of entropic polymatroids which can be formulated as gluability conditions of the polymatroid to an identical copy of itself along arbitrary restrictions and such that the two pieces are independent given the common restriction. We show that positive definite matrices satisfy this condition as well and examine consequences for Gaussian conditional independence structures. New axioms of Gaussian CI are obtained by applying selfadhesivity to the previously known axioms of structural semigraphoids and orientable gaussoids.

翻译：自粘性是熵多拟阵的一个性质，可表述为该多拟阵沿任意限制条件与其自身副本的粘合性条件，且两个部分在给定共同限制时相互独立。我们证明正定矩阵同样满足该条件，并探讨其对高斯条件独立结构的推论。通过将自粘性应用于结构半拟阵和可定向高斯拟阵的已知公理，获得了高斯CI的新公理。