论文标题
多层的尖锐的log-sobolev不平等
A sharp log-Sobolev inequality for the multislice
论文作者
论文摘要
我们确定具有任意参数的多重肌肉bernoulli-laplace扩散模型的log-sobolev常数，直至一个小的通用乘法常数。我们的结果扩展了对Lee and Yau（1998）的经典估计，并确认了Filmus，O'Donnell和Wu（2018）的猜想。在其他应用中，我们完全量化了多层上的“小型扩展”现象，并在各种图上获得彩色排除过程的尖锐混合时间估计。
We determine the log-Sobolev constant of the multi-urn Bernoulli-Laplace diffusion model with arbitrary parameters, up to a small universal multiplicative constant. Our result extends a classical estimate of Lee and Yau (1998) and confirms a conjecture of Filmus, O'Donnell and Wu (2018). Among other applications, we completely quantify the "small-set expansion" phenomenon on the multislice, and obtain sharp mixing-time estimates for the colored exclusion process on various graphs.
