Selfadhesivity is a property of entropic polymatroids which guarantees that the polymatroid can be glued to an identical copy of itself along arbitrary restrictions 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，它保证该多拟阵可以沿着任意限制与其自身的相同副本粘合，使得两个部分在给定共同限制的条件下相互独立。我们证明正定矩阵也满足这一条件，并考察了由此对高斯条件独立结构的影响。通过将自粘性应用于先前已知的结构半图拟阵和可定向高斯体的公理，我们得到了高斯条件独立性的新公理。