论文标题
在圆圈上混合tasep的时间
Mixing times for the TASEP on the circle
论文作者
论文摘要
我们研究了与$ k $颗粒的长度$ n $圆圈中完全不对称的简单排除过程（TASEP）的混合时间。我们表明，混合时间为$ n^2 \ min（k，n-k）^{ - 1/2} $，并且不会发生截止现象。这证实了Jara，Lacoin和Peres分别预测的行为，并且更广泛地认为它可以在KPZ-Universalty类中具有可综合模型。我们的论点依赖于与周期性最后一段渗透的联系，对平坦的大地测量学进行了详细分析，以及新的随机扩展和时间转移论证，以期为上次段落渗透。
We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a circle of length $N$ with $k$ particles. We show that the mixing time is of order $N^2 \min(k,N-k)^{-1/2}$, and that the cutoff phenomenon does not occur. This confirms behavior which was separately predicted by Jara, Lacoin and Peres, and it is more broadly believed to hold for integrable models in the KPZ-universalty class. Our arguments rely on a connection to periodic last passage percolation with a detailed analysis of flat geodesics, as well as a novel random extension and time shift argument for last passage percolation.
