Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II
Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II
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DOI：
10.1142/s1793525321500461
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发表时间：
2021
影响因子：
0.8
通讯作者：
Michael Brannan;Li Gao;M. Junge
中科院分区：
文献类型：
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作者：
Michael Brannan;Li Gao;M. Junge
我们研究了之前由Junge，Li和Laracuente提出的“几何Ricci曲率下界”，对于各种例子，包括群von Neumann代数，自由正交量子群[公式：见文本]，[公式：见文本]-变形的高斯代数和量子环面。特别地，我们证明了[Formula：See Text]上的Laplace算子通过经典正交群上的Laplace-Beltrami算子允许因子分解，从而在这两个算子之间建立了第一个联系。基于非负曲率条件，我们得到了上述例子中相应量子马尔可夫半群的修正的LOG-Soblev不等式的完全有界形式。我们还证明了几何Ricci曲率下界在张量积和合并自由积下是稳定的。作为应用，我们得到了自由群因子上的字长半群的一个锐利的Ricci曲率下界。
We study the “geometric Ricci curvature lower bound”, introduced previously by Junge, Li and LaRacuente, for a variety of examples including group von Neumann algebras, free orthogonal quantum groups [Formula: see text], [Formula: see text]-deformed Gaussian algebras and quantum tori. In particular, we show that Laplace operator on [Formula: see text] admits a factorization through the Laplace–Beltrami operator on the classical orthogonal group, which establishes the first connection between these two operators. Based on a non-negative curvature condition, we obtain the completely bounded version of the modified log-Sobolev inequalities for the corresponding quantum Markov semigroups on the examples mentioned above. We also prove that the “geometric Ricci curvature lower bound” is stable under tensor products and amalgamated free products. As an application, we obtain a sharp Ricci curvature lower bound for word-length semigroups on free group factors.