Mass Transportation Proofs of Free Functional Inequalities, and Free Poincare Inequalities
Mass Transportation Proofs of Free Functional Inequalities, and Free Poincare Inequalities
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自由函数不等式和自由庞加莱不等式的公共交通证明
DOI：
10.1016/j.jfa.2009.03.011
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Ionel Popescu
中科院分区：
文献类型：
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作者：
M. Ledoux;Ionel Popescu
这项工作致力于一维自由概率背景下函数不等式族的直接大众运输证明，避免随机矩阵近似。不等式包括自由形式的传输、Log-Sobolev、HWI 插值和严格凸势的 Brunn-Minkowski 不等式。提出了夏普常数和一些扩展版本。该论文还讨论了自由庞加莱不等式的两个版本及其对雅可比算子谱特性的解释。最后一部分以 Marcenko–Pastur 分布的参考示例建立了 R+ 测度的相应不等式。
This work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the transportation, Log-Sobolev, HWI interpolation and Brunn–Minkowski inequalities for strictly convex potentials. Sharp constants and some extended versions are put forward. The paper also addresses two versions of free Poincaré inequalities and their interpretation in terms of spectral properties of Jacobi operators. The last part establishes the corresponding inequalities for measures on R+with the reference example of the Marcenko–Pastur distribution.