标题： 与Wishart随机矩阵对角块行列式的高斯乘积不等式猜想相关的结果 显示英文标题

标题： Results related to the Gaussian product inequality conjecture for determinants of diagonal blocks of Wishart random matrices

摘要： 在本文中，将与高斯乘积不等式（GPI）猜想相关的各种结果，从Wei（2014）、Genest & Ouimet（2023）和Zhou等人（2023）的结果推广到Wishart随机矩阵的对角块行列式的设置中。 通过其分布为二阶多元全正相关（MTP 2），也展示了GPI的一种扩展形式适用于Wishart随机矩阵的特征值。 作为最后的思考，提出了一条新的未被探索的研究途径，从椭圆分布的角度研究GPI。 显示英文摘要

摘要： In this paper, various results related to the Gaussian product inequality (GPI) conjecture, from Wei (2014), Genest & Ouimet (2023) and Zhou et al. (2023), are generalized to the setting of determinants of diagonal blocks of Wishart random matrices. An extended form of the GPI is also shown to hold for the eigenvalues of Wishart random matrices by virtue of their law being multivariate totally positive of order 2 (MTP 2). As final thoughts, a new unexplored avenue of research is presented to study the GPI from the point of view of elliptical distributions.