论文标题
通过RICCI曲率界限II的完整对数Sobolev不平等现象
Complete Logarithmic Sobolev Inequalities via Ricci Curvature Bounded Below II
论文作者
论文摘要
使用非负曲率条件，我们证明了在各种紧凑型量子组上的中央马尔可夫半群的修改log-sobolev不平等的完整版本，包括组von Neumann代数，自由正交组和量子自动构成组。我们还证明，在张量和合并的免费产品下，Junge-Li-Laracuente引入的“几何RICCI曲率下限”是稳定的。作为应用程序，我们获得了关于自由组因子和合并的免费产品代数的单词长度半群的几何曲率下限和完整修改的对数Sobolev不等式。
Using a non-negative curvature condition, we prove the complete version of modified log-Sobolev inequalities for central Markov semigroups on various compact quantum groups, including group von Neumann algebras, free orthogonal group and quantum automorphism groups. We also prove that the "geometric Ricci curvature lower bound" introduced by Junge-Li-LaRacuente is stable under tensor products and amalgamated free products. As an application, we obtain the geometric Ricci curvature lower bound and complete modified logarithmic Sobolev inequality for word-length semigroups on free group factors and amalgamated free product algebras.
