A new asymmetric correlation inequality for Gaussian measure
Résumé
The Khatri-\v{S}id\'{a}k lemma says that for any Gaussian measure μ over Rn , given a convex set K and a slab L, both symmetric about the origin, one has μ(K∩L)≥μ(K)μ(L). We state and prove a new asymmetric version of the Khatri-\v{S}id\'{a}k lemma when K is a symmetric convex body and L is a slab (not necessarily symmetric about the barycenter of K). Our result also extends that of Szarek and Werner (1999), in a special case.
Origine | Fichiers produits par l'(les) auteur(s) |
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