发表机构
University of Washington; Yale University（华盛顿大学; 耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明无条件对数凹测度的无维数Poincaré不等式，从而在无条件情形下解决KLS猜想，方法结合Dunkl算子理论与测度变换及谱分析，核心思想由AI辅助生成。
AI 中文摘要
我们证明了各向同性无条件对数凹概率测度的无维数Poincaré不等式，在无条件情形下建立了Kannan-Lovász-Simonovits（KLS）猜想。证明结合了Dunkl算子理论的新应用以及对数凹测度的适当变换。具体而言，证明通过对适应于变换后测度的新Dunkl-Langevin算子进行直接谱分析来完成。证明的核心思想是由AI生成工具在与作者的数周互动中产生。作者对论证进行了精炼和形式化。
英文摘要
We prove a dimension-free Poincaré inequality for isotropic unconditional log-concave probability measures, establishing the Kannan-Lovász-Simonovits (KLS) conjecture in the unconditional setting. The proof combines a new application of Dunkl operator theory combined with an appropriate transformation of the log-concave measure. Specifically, the proof follows by a direct spectral analysis of a new Dunkl-Langevin operator adapted to the transformed measure. The core ideas of the proof were generated by AI generative tools through interactions with the authors over several weeks. The authors refined and formalized the argument.
Comments33 pages, 1 figure
