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Logarithmic Sobolev and Poincaré inequalities for the circular Cauchy distribution


 
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1. Title Title of document Logarithmic Sobolev and Poincaré inequalities for the circular Cauchy distribution
 
2. Creator Author's name, affiliation, country Yutao Ma; Beijing Normal University; China
 
2. Creator Author's name, affiliation, country Zhengliang Zhang; Wuhan University; China
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) circular Cauchy distribution, spectral gap,logarithmic Sobolev inequalities
 
3. Subject Subject classification 60E15,39B62,26Dxx
 
4. Description Abstract In this paper, consider the circular Cauchy distribution $\mu_x$ on the unit circle $S$ with index $0\le |x|<1$, we study the spectral gap and the optimal logarithmic Sobolev constant  for $\mu_x$, denoted respectively as $\lambda_1(\mu_x)$ and $C_{\mathrm{LS}}(\mu_x).$ We prove that $\frac{1}{1+|x|}\le \lambda_1(\mu_x)\le 1$ while $C_{\mathrm{LS}}(\mu_x)$ behaves like $\log(1+\frac{1}{1-|x|})$ as $|x|\to 1.$
 
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7. Date (YYYY-MM-DD) 2014-02-18
 
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/3071
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3071
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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