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Logarithmic Sobolev and Poincaré inequalities for the circular Cauchy distribution
2014
Electronic Communications in Probability
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.
doi:10.1214/ecp.v19-3071
fatcat:xt6jymc27jalbbxt3fc3hbizxa