PreprintCC BY 4.0arXiv
Sharp logarithmic Sobolev inequalities on free groups by variational comparison
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.
Related
- Sharp Logarithmic Sobolev Inequalities for q-Araki-Woods Ornstein-Uhlenbeck Semigroups
- Sharp quantum logarithmic Sobolev inequalities via semigroup interpolation
- Complete Modified Logarithmic Sobolev Inequalities for one-dimensional quantum Spin Chain
- Generalized Logarithmic Sobolev inequalities on Bounded Domains and exponential decay to Boltzmann states for Nernst--Planck--Navier--Stokes systems
- Ground states and sharp logarithmic Sobolev inequalities for logarithmic Schrödinger equations with partial confinement
BibTeX
@misc{yao2026sharp,
title = {{Sharp logarithmic Sobolev inequalities on free groups by variational comparison}},
author = {Gan Yao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17303},
eprint = {2609.17303},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17303},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp logarithmic Sobolev inequalities on free groups by variational comparison
AU - Gan Yao
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17303
UR - https://arxiv.org/abs/2609.17303
AB - 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.
ER -