Royen's proof of the Gaussian correlation inequality
Rafał Latała, Dariusz Matlak
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Abstract
We present in detail Thomas Royen's proof of the Gaussian correlation inequality which states that $μ(K\cap L)\geq μ(K)μ(L)$ for any centered Gaussian measure $μ$ on $R^d$ and symmetric convex sets $K,L$ in $R^d$.
arXiv comments
9 pages
Journal reference
Geometric Aspects of Functional Analysis, Israel Seminar (GAFA) 2014-2016, 265-275, Lecture Notes in Math. 2169, Springer 2017
Here is a blog post that I think clarifies why this conjecture had remained unsolved: https://almostsure.wordpress.com/2009/09/27/the-gaussian-cor... There is also a 'companion' article on arxiv that provides a clear presentation of Royen's proof: https://arxiv.org/abs/1512.08776
Here is a blog post that I think clarifies why this conjecture had remained unsolved: https://almostsure.wordpress.com/2009/09/27/the-gaussian-cor... There is also a 'companion' article on arxiv that provides a clear presentation of Royen's proof: https://arxiv.org/abs/1512.08776
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