Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality

2022/08/30 by Russell, Oliver, Sun, Wei · 1 citation
#FOS: Mathematics #Primary 60E15 #Probability (math.PR) #Secondary 62H12

paper · doi:10.48550/arxiv.2208.13957

Abstract

We prove the three-dimensional Gaussian product inequality (GPI) E[X₁²X₂^2m₂X₃^2m₃]≥ E[X₁²]E[X₂^2m₂]E[X₃^2m₃] for any centered Gaussian random vector (X₁,X₂,X₃) and m₂,m₃∈ℕ. We discover a novel inequality for the moment ratio \frac|E[ X₂^2m₂+1X₃^2m₃+1]|E[ X₂^2m₂X₃^2m₃], which implies the 3D-GPI. The interplay between computing and hard analysis plays a crucial role in the proofs.

Cited by

• Results related to the Gaussian product inequality conjecture for mixed-sign exponents in arbitrary dimension

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