论文标题
排除水库的截止的通用性
Universality of cutoff for exclusion with reservoirs
论文作者
论文摘要
我们考虑使用任意网络上的储层的可逆排除过程。我们根据基础网络的某些简单统计数据来表征该过程的光谱差距，混合时间和混合窗口。除其他后果外，我们还建立了Aldous光谱间隙猜想的非保守类似物，并且只有在满足产品条件时才出现截止时间。我们通过在任意维度和边界条件的离散晶格上提供明确的截止，从而大大概括了最近的一维结果，从而说明了这一点。我们还获得了相对熵，希尔伯特规范，分离距离和至上规范的截止现象。我们的证明以一种新颖的简单方法利用了负面依赖，以将对整个过程的理解减少到单位边缘的理解。我们认为，这种方法会找到其他应用程序。
We consider the reversible exclusion process with reservoirs on arbitrary networks. We characterize the spectral gap, mixing time, and mixing window of the process, in terms of certain simple statistics of the underlying network. Among other consequences, we establish a non-conservative analogue of Aldous's spectral gap conjecture, and we show that cutoff occurs if and only if the product condition is satisfied. We illustrate this by providing explicit cutoffs on discrete lattices of arbitrary dimensions and boundary conditions, which substantially generalize recent one-dimensional results. We also obtain cutoff phenomena in relative entropy, Hilbert norm, separation distance and supremum norm. Our proof exploits negative dependence in a novel, simple way to reduce the understanding of the whole process to that of single-site marginals. We believe that this approach will find other applications.
