Some New Results on Gaussian Product Inequalities

2023/08/26 by Zhou, Qian-Qian, Zhao, Han, Hu, Ze-Chun +1 · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2308.13740

Abstract

The long-standing Gaussian product inequality (GPI) conjecture states that, for any centered ℝⁿ-valued Gaussian random vector (X₁, …, X_n) and any positive reals α₁, …, α_n, \bf E[∏_j=1ⁿ|X_j|^α_j]≥ ∏_j=1ⁿ\bf E[|X_j|^α_j]. In this paper, we present some related inequalities for centered ℝⁿ-valued Gaussian random vector (X₁, …, X_n) when \α₁, …, α_n\ contains both positive and negative numbers.

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

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