Teheranchi's strong Gaussian correlation conjecture for symmetric convex sets

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Let d>0d>0 and let K,T⊆RdK,T\subseteq \mathbb R^d be origin-symmetric convex sets, and let γd\gamma_d denote the usual Gaussian probability measure. Teheranchi's strong Gaussian correlation conjecture.

γd(K+T)γd(K∩T)≥γd(K)γd(T).\gamma_d(K+T)\gamma_d(K\cap T)\ge \gamma_d(K)\gamma_d(T).

This geometric formulation strengthens Royen's Gaussian correlation inequality and was conjectured by Teheranchi. The paper presents it as a weaker inequality than the slab-based geometric refinement, but its general validity remains open.

References

Primary source

Rotem Assouline, Arnon Chor and Shay Sadovsky, “A refinement of the Šidák-Khatri inequality and a strong Gaussian correlation conjecture”, arXiv:2407.15684 (2024).

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