自由群上通过变分比较的尖锐对数Sobolev不等式

中文摘要 AI 辅助

我们给出了自由群冯·诺依曼代数上词长Poisson半群的常数为$2$的尖锐对数Sobolev不等式的变分比较证明。我们的方法将[Yao26]中循环群的Lagrange方法推广到有限迹冯·诺依曼代数的框架中。该不等式最近由Xie和Zhang在[XZ26]中通过完全不同的方法建立。

英文摘要

We give a variational comparison proof of the sharp logarithmic Sobolev inequality with constant $2$ for the word-length Poisson semigroup on free group von Neumann algebras. Our approach extends the Lagrange method for cyclic groups in [Yao26] to a framework in finite tracial von Neumann algebras. The inequality was recently established by Xie and Zhang in [XZ26] using a completely different approach.

发表机构

• Institute for Advanced Study in Mathematics, Harbin Institute of Technology（哈尔滨工业大学数学高等研究院）

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