Logarithmic Sobolev inequalities for generalised Cauchy measures
Inégalité de Sobolev logarithmique pour les mesures de Cauchy généralisées
Résumé
We prove a curvature-dimension criterion and obtain logarithmic Sobolev inequalities for generalised Cauchy measures with optimal weights and explicit constants. In the one-dimensional case, this constant is even optimal. From these inequalities, we derive concentration results, which allow concluding the case of the pathological dimension two.
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