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Preprints, Working Papers, ... Year : 2016

A new asymmetric correlation inequality for Gaussian measure

Abstract

The Khatri-\v{S}id\'{a}k lemma says that for any Gaussian measure $\mu$ over $\mathbb{R}^n$ , given a convex set $K$ and a slab $L$, both symmetric about the origin, one has $\mu(K \cap L) \geq \mu(K)\mu(L)$. 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.
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Dates and versions

hal-01360457 , version 1 (05-09-2016)

Identifiers

  • HAL Id : hal-01360457 , version 1

Cite

Kunal Dutta, Arijit Ghosh, Nabil Mustafa. A new asymmetric correlation inequality for Gaussian measure. 2016. ⟨hal-01360457⟩
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