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

Key Points

• 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.