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.

Automated summary

This paper presents some related inequalities for the Gaussian product inequality when both positive and negative numbers are included.