October 16, 2025Open Access

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

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The study confirms that the Gaussian product inequality holds for varying exponents, including both positive and negative.
A quantitative lower bound is achieved, conditional on the validity of the Gaussian product inequality conjecture.
This research extends previous findings by demonstrating the inequality's consistency in arbitrary dimensions.
Conditional results suggest ongoing exploration is needed to validate conjectures associated with this inequality.

Implication

Note establishes the Gaussian product inequality across dimensions, highlighting mixed-sign exponents.

Abstract

This note establishes that the opposite Gaussian product inequality (GPI) of the type proved by Russell & Sun (2022a) in two dimensions, and partially extended to higher dimensions by Zhou et al. (2024), continues to hold for an arbitrary mix of positive and negative exponents. A general quantitative lower bound is also obtained conditionally on the GPI conjecture being true.

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Cite This Study

Lan et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd259 https://doi.org/10.48550/arxiv.2505.09976

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Implication

Note establishes the Gaussian product inequality across dimensions, highlighting mixed-sign exponents.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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