Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study the semi-algebraic geometry of these models, in particular their dimension, smoothness and connectedness. Results on their vanishing ideals and conditional independence ideals are also included, and we put them into the general framework of conditional independence models. We end with several open questions and conjectures.

翻译：Gausian 双倍的Markovian 模型包括共变矩阵,由一对图表限制,在共变矩阵中同时指定零及其反向。我们研究了这些模型的半代数几何结构,特别是其尺寸、平稳和关联性。这些模型的消失理想和有条件独立理想的结果也被包括在内,我们将其纳入有条件独立模型的总框架。我们最后提出几个开放的问题和推测。