Logarithmic Sobolev inequalities for generalised Cauchy measures
Functional Analysis
2026-04-06 v2 Probability
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.
Cite
@article{arxiv.2411.17239,
title = {Logarithmic Sobolev inequalities for generalised Cauchy measures},
author = {Baptiste Nicolas Huguet},
journal= {arXiv preprint arXiv:2411.17239},
year = {2026}
}