Abstract
We prove the three-dimensional Gaussian product inequality (GPI)E[X12X22m2X32m3]≥E[X12]E[X22m2]E[X32m3] for any centered Gaussian random vector (X1,X2,X3) and m2,m3∈N. We discover a novel inequality for the moment ratio |E[X22m2+1X32m3+1]|E[X22m2X32m3], which implies the 3D-GPI. The interplay between computing and hard analysis plays a crucial role in the proofs.
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