论文标题
在一部分上的ASEP截止曲线
Cutoff profile of ASEP on a segment
论文作者
论文摘要
本文研究了长度$ n $的一部分上的不对称简单排除过程（ASEP）的混合行为。我们的主要结果是，对于$（0,1）中的粒子密度，$ $ n^{1/3} $的总变量截止窗口为$ 1-f _ {\ mathrm {gue}}，$ f _ {\ f _ {\ mathrm {\ mathrm {gue}} $是tracy-wism-wism-wism-wism-wism formation formation。这也提供了截止本身的新证明，Labbé和LaCoin早些时候显示了。我们的证明结合了耦合参数，这是关于ASEP波动的Tracy-Widom的结果，从步骤初始条件开始，而确切的代数身份来自将多物种ASEP解释为Hecke代数上的随机步行。
This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length $N$. Our main result is that for particle densities in $(0,1),$ the total-variation cutoff window of ASEP is $N^{1/3}$ and the cutoff profile is $1-F_{\mathrm{GUE}},$ where $F_{\mathrm{GUE}}$ is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbé and Lacoin. Our proof combines coupling arguments, the result of Tracy-Widom about fluctuations of ASEP started from the step initial condition, and exact algebraic identities coming from interpreting the multi-species ASEP as a random walk on a Hecke algebra.
