Logarithmic Sobolev and Poincaré inequalities for the circular Cauchy distribution ∗
نویسندگان
چکیده
In this paper, we consider the circular Cauchy distribution μx on the unit circle S with index 0 ≤ |x| < 1 and we study the spectral gap and the optimal logarithmic Sobolev constant for μx, denoted respectively by λ1(μx) and CLS(μx). We prove that 1 1+|x| ≤ λ1(μx) ≤ 1 while CLS(μx) behaves like log(1 + 1 1−|x| ) as |x| → 1.
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تاریخ انتشار 2014