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 $|x|\to 1.$ |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | |
7. | Date | (YYYY-MM-DD) | 2014-02-18 |
8. | Type | Status & genre | Peer-reviewed Article |
8. | Type | Type | |
9. | Format | File format | |
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 |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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