Logarithmic Sobolev inequalities for generalised Cauchy measures

2024/11/26 by Huguet, Baptiste Nicolas
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2411.17239

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.

Related

• Modified logarithmic Sobolev inequalities on R
• Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality
• Some remarks on weighted logarithmic Sobolev inequality
• Moment estimates implied by modified log-Sobolev inequalities
• Concentration of measures supported on the cube