论文标题
在高密度和低密度阶段混合时间和截止
Mixing times and cutoff for the TASEP in the high and low density phase
论文作者
论文摘要
我们研究具有高密度和低密度相的开放边界的完全不对称的简单排除过程。在这两个阶段的大部分中，我们表明，长度为$ n $的一部分的过程以$ n $的订单显示截止，而在阶段的交集，共存线，混合时间为$ n^2 $，不发生cutoff。特别是，我们确定共存中的$ \ varepsilon $ - 混合时间，直至不变因素，这不取决于$ \ varepsilon $。结合最大电流阶段的先前结果，这可以通过开放边界完成TASEP的混合时间。
We study the totally asymmetric simple exclusion process with open boundaries in the high density and the low density phase. In the bulk of the two phases, we show that the process on a segment of length $N$ exhibits cutoff at order $N$, while in the intersection of the phases, the coexistence line, the mixing time is of order $N^2$, and no cutoff occurs. In particular, we determine the $\varepsilon$-mixing time in the coexistence line up to constant factors, which do not dependent on $\varepsilon$. Combined with previous results on the maximal current phase, this completes the picture on mixing times for the TASEP with open boundaries.
