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2011 Gaussian measures of dilations of convex rotationally symmetric sets in $\mathbb{C}^n$
Tomasz Tkocz
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Electron. Commun. Probab. 16: 38-49 (2011). DOI: 10.1214/ECP.v16-1599

Abstract

We consider the complex case of the S-inequality. It concerns the behaviour of Gaussian measures of dilations of convex and rotationally symmetric sets in $\mathbb{C}^n$. We pose and discuss a conjecture that among all such sets measures of cylinders decrease the fastest under dilations. Our main result in this paper is that this conjecture holds under the additional assumption that the Gaussian measure of the sets considered is not greater than some constant $c > 0.64$.

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Tomasz Tkocz. "Gaussian measures of dilations of convex rotationally symmetric sets in $\mathbb{C}^n$." Electron. Commun. Probab. 16 38 - 49, 2011. https://doi.org/10.1214/ECP.v16-1599

Information

Accepted: 12 January 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1225.60059
MathSciNet: MR2763527
Digital Object Identifier: 10.1214/ECP.v16-1599

Subjects:
Primary: 60E15
Secondary: 60G15

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