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On Repeated Sequential Closures of Constructible Functions in Valuations Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Royen’s Proof of the Gaussian Correlation Inequality

Authors : Rafał Latała, Dariusz Matlak

Published in: Geometric Aspects of Functional Analysis

Publisher: Springer International Publishing

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Abstract

We present in detail Thomas Royen’s proof of the Gaussian correlation inequality which states that μ(K ∩ L) ≥ μ(K)μ(L) for any centered Gaussian measure μ on \(\mathbb{R}^{d}\) and symmetric convex sets K, L in \(\mathbb{R}^{d}\).

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previous chapter Rigidity of the Chain Rule and Nearly Submultiplicative Functions
next chapter A Simple Tool for Bounding the Deviation of Random Matrices on Geometric Sets
Literature
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G. Qingyang, The Gaussian correlation inequality for symmetric convex sets. arXiv:1012.0676 (2010)
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T. Royen, A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions. Far East J. Theor. Stat. 48, 139–145 (2014)MathSciNetMATH
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Metadata
Title
Royen’s Proof of the Gaussian Correlation Inequality
Authors
Rafał Latała
Dariusz Matlak
Copyright Year
2017
Book
Geometric Aspects of Functional Analysis

Print ISBN: 978-3-319-45281-4

Electronic ISBN: 978-3-319-45282-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-45282-1_17

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