论文标题
将MLSI升级到LSI，以进行可逆的马尔可夫链
Upgrading MLSI to LSI for reversible Markov chains
论文作者
论文摘要
For reversible Markov chains on finite state spaces, we show that the modified log-Sobolev inequality (MLSI) can be upgraded to a log-Sobolev inequality (LSI) at the surprisingly low cost of degrading the associated constant by $\log (1/p)$, where $p$ is the minimum non-zero transition probability.我们通过为任意图上的零范围过程提供第一个Log-Sobolev估算来说明这一点。作为另一个应用程序，我们确定了所有有限度图上lamplighter链的修改后的log-sobolev常数，并使用它为Montenegro和Tetali（2006）和Hermon and Peres（2018）的两个开放问题提供负面答案。我们的证明基于最近两位作者最近引入的“正则化技巧”。
For reversible Markov chains on finite state spaces, we show that the modified log-Sobolev inequality (MLSI) can be upgraded to a log-Sobolev inequality (LSI) at the surprisingly low cost of degrading the associated constant by $\log (1/p)$, where $p$ is the minimum non-zero transition probability. We illustrate this by providing the first log-Sobolev estimate for Zero-Range processes on arbitrary graphs. As another application, we determine the modified log-Sobolev constant of the Lamplighter chain on all bounded-degree graphs, and use it to provide negative answers to two open questions by Montenegro and Tetali (2006) and Hermon and Peres (2018). Our proof builds upon the `regularization trick' recently introduced by the last two authors.
