论文标题
大都市有偏见的临界值
Cutoff profile of the Metropolis biased card shuffling
论文作者
论文摘要
我们考虑大都市有偏的卡片（也称为有限间隔或随机大都市扫描的多物种ASEP）。据信，它与固定的融合表现出了总变化的截止，并且几年前由Labbé和Lacoin证明。在本文中，我们证明（对于$ n $卡）截止窗口的顺序为$ n^{1/3} $，并且截止配置文件由Goe Tracy-Widom分发功能给出。这证实了Bufetov和Nejjar的猜想。我们的方法与Labbé-LaCoin不同，通过将卡片的缩减与$ \ Mathbb {z} $上的多种物种ASEP进行比较，并使用Hecke代数以及最近的ASEP Shift-Shift-Invarianciance和Convergence结果。我们的结果也可以看作是Bufetov-Gorin-Romik的定向交换过程的概括，这是Tasep版本（我们的结果）。
We consider the Metropolis biased card shuffling (also called the multi-species ASEP on a finite interval or the random Metropolis scan). Its convergence to stationary was believed to exhibit a total-variation cutoff, and that was proved a few years ago by Labbé and Lacoin. In this paper, we prove that (for $N$ cards) the cutoff window is in the order of $N^{1/3}$, and the cutoff profile is given by the GOE Tracy-Widom distribution function. This confirms a conjecture by Bufetov and Nejjar. Our approach is different from Labbé-Lacoin, by comparing the card shuffling with the multi-species ASEP on $\mathbb{Z}$, and using Hecke algebra and recent ASEP shift-invariance and convergence results. Our result can also be viewed as a generalization of the Oriented Swap Process finishing time convergence of Bufetov-Gorin-Romik, which is the TASEP version (of our result).
