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


 
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1. Title Title of document Gaussian measures of dilations of convex rotationally symmetric sets in $\mathbb{C}^n$
 
2. Creator Author's name, affiliation, country Tomasz Tkocz; University of Warsaw
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian measure, convex bodies, isoperimetric inequalities
 
3. Subject Subject classification Primary 60E15; Secondary 60G15
 
4. Description 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 $c > 0.64$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-01-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1599
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1599
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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