Optimal Weighted Poincaré and Log-Sobolev Inequalities for Cauchy Measures

2010/10/25 by Zhengliang Zhang, Bin Qian, Zhang, Zhengliang +3
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1010.5043

This paper has been withdrawn by the author due to a crucial error

openalex publication_date 2010/10/25 · arxiv created 2011/03/22 · arxiv updated 2011/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, We establish the weighted Poincaré inequalities and Log-Sobolev inequalities for Cauchy distributions with optimal weight functions.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
• Logarithmic Sobolev Inequalities

Related

• Some remarks on weighted logarithmic Sobolev inequality
• Logarithmic Sobolev inequalities for generalised Cauchy measures
• Transport proofs of weighted Poincaré inequalities for log-concave distributions
• Weighted Super Poincare Inequalities for Infinite-Dimensional Extension of the Dirichlet Distribution
• From Super Poincaré to Weighted Log-Sobolev and Entropy-Cost Inequalities