论文标题
多项式协方差的高斯产品不平等猜想
The Gaussian product inequality conjecture for multinomial covariances
论文作者
论文摘要
在此简短说明中，我们发现等效的组合条件仅涉及有限总和，在该总和下，具有多项式协方差矩阵的中心高斯随机矢量满足高斯产品不平等（GPI）的猜想。这些协方差矩阵很重要，因为它们的非对角线元素为负，这是GPI猜想的最难案例，如[Russell，O。，\＆Sun，W。2022。 {\ em J. Math。肛门。 appl。}，{\ bf 515}（2），纸编号126439，21 pp。]。
In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These covariance matrices are relevant since their off-diagonal elements are negative, which is the hardest case to cover for the GPI conjecture, as mentioned by [Russell, O., \& Sun, W. 2022. Some new {G}aussian product inequalities. {\em J. Math. Anal. Appl.}, {\bf 515}(2), Paper No. 126439, 21 pp.].
