2022/09/03 by Frédéric Ouimet, Ouimet, Frédéric
Mathematics · #05A20 #60E15 #62E20 62H10 #FOS: Mathematics #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2209.01505
openalex publication_date 2022/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Gaussian product inequalities. \em J. Math. Anal. Appl., \bf 515(2), Paper No. 126439, 21 pp.].