Some new results on Gaussian product inequalities

The long-standing Gaussian product inequality (GPI) conjecture states that, for any centered Rn-valued Gaussian random vector (X1, ... , Xn) and any positive reals alpha 1, . . . , alpha n, E[pi nj=1 |Xj |alpha j] >= pi n j=1 E[|Xj|alpha j]. In this paper, we present some related inequalities for centered Rn-valued Gaussian random vector (X1, ... , Xn) when {alpha 1, . . . , alpha n} contains both positive and negative numbers.(c) 2023 Elsevier Inc. All rights reserved.