## Electronic Communications in Probability

### Gaussian measures of dilations of convex rotationally symmetric sets in $\mathbb{C}^n$

Tomasz Tkocz

#### 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 $c > 0.64$.

#### Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 5, 38-49.

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

https://projecteuclid.org/euclid.ecp/1465261961

Digital Object Identifier
doi:10.1214/ECP.v16-1599

Mathematical Reviews number (MathSciNet)
MR2763527

Zentralblatt MATH identifier
1225.60059

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60G15: Gaussian processes

Rights
Tkocz, Tomasz. Gaussian measures of dilations of convex rotationally symmetric sets in $\mathbb{C}^n$. Electron. Commun. Probab. 16 (2011), paper no. 5, 38--49. doi:10.1214/ECP.v16-1599. https://projecteuclid.org/euclid.ecp/1465261961