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- W2123238672 abstract "In this paper, consider the circular Cauchy distribution $mu_x$ on the unit circle $S$ with index $0le |x|<1$, 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 $|x|to 1.$" @default.
- W2123238672 created "2016-06-24" @default.
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- W2123238672 date "2014-01-01" @default.
- W2123238672 modified "2023-09-23" @default.
- W2123238672 title "Logarithmic Sobolev and Poincaré inequalities for the circular Cauchy distribution" @default.
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- W2123238672 doi "https://doi.org/10.1214/ecp.v19-3071" @default.
- W2123238672 hasPublicationYear "2014" @default.
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