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arXiv · 2411.17239

Logarithmic Sobolev inequalities for generalised Cauchy measures

Baptiste Nicolas Huguet
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Abstract

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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Baptiste Nicolas Huguet. 2024-11-26. Logarithmic Sobolev inequalities for generalised Cauchy measures. https://arxiv.org/abs/2411.17239

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