Logarithmic Sobolev and Poincare inequalities for the circular Cauchy distribution

被引：6
|
作者：
Ma, Yutao [1 ,2 ]
Zhang, Zhengliang [3 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
[2] Beijing Normal Univ, Lab Math Com Sys, Beijing 100875, Peoples R China
[3] Wuhan Univ, Dept Math & Stat, Wuhan, Peoples R China
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2014年 / 19卷
关键词：
circular Cauchy distribution; spectral gap; logarithmic Sobolev inequality; TRANSPORTATION COST; EIGENVALUE;
D O I：
10.1214/ECP.v19-3071
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, we consider the circular Cauchy distribution mu(x) on the unit circle S with index 0 <= vertical bar x vertical bar < 1 and we study the spectral gap and the optimal logarithmic Sobolev constant for mu(x), denoted respectively by lambda(1)(mu(x)) and C-LS (mu(x)). We prove that 1/1+vertical bar x vertical bar <= lambda(1)(mu(x)) <= 1 while C-LS (mu(x)) behaves like log (1+1/1-vertical bar x vertical bar) as vertical bar x vertical bar -> 1.
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页码：1 / 9
页数：9
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