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arXiv · 2609.17303

Sharp logarithmic Sobolev inequalities on free groups by variational comparison

Gan Yao
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Abstract

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.

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Gan Yao. 2026-09-15. Sharp logarithmic Sobolev inequalities on free groups by variational comparison. https://arxiv.org/abs/2609.17303

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