Logarithmic Sobolev inequalities for generalised Cauchy measures

Published 26 Nov 2024 in math.FA and math.PR | (2411.17239v1)

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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Authors (1)

Baptiste Nicolas Huguet

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