A refinement of the Šidák-Khatri inequality and a strong Gaussian correlation conjecture (2407.15684v1)

Abstract: We prove two special cases of a strengthened Gaussian correlation conjecture, due to Tehranchi, and show that if the conjecture holds asymptotically, it holds for any dimension. Additionally, we use these special cases to prove a refined version of the \v{S}id\'ak-Khatri inequality.