论文标题
通过马尔可夫链的硬球的相关衰减
Correlation decay for hard spheres via Markov chains
论文作者
论文摘要
我们在两个及更高尺寸的硬球模型的临界延期和临界密度上的所有已知下限改进。由于尺寸倾向于无限，我们的改进分别按$ 2 $和$ 1.7 $的因素。我们通过利用理论计算机科学的技术来实现这些改进，以表明从硬球模型采样的一定的马尔可夫链以足够低的露天率迅速混合。然后，我们证明了最佳的空间和时间混合之间的等效性，以推断出我们的结果。
We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions two and higher. As the dimension tends to infinity our improvements are by factors of $2$ and $1.7$, respectively. We make these improvements by utilizing techniques from theoretical computer science to show that a certain Markov chain for sampling from the hard sphere model mixes rapidly at low enough fugacities. We then prove an equivalence between optimal spatial and temporal mixing for hard spheres to deduce our results.
