ASEP中第二类质点的极限速度
Limiting speed of a second class particle in ASEP
摘要：
研究了$\mathbb{Z}$上两种群非对称简单排它过程（ASEP）中第二类粒子的渐近速度.对于任意固定的非负整数$L$，我们考虑从初始数据开始的两种群ASEP，其中$\mathbb{Z}_{<-L}$的所有位置被第一类粒子占据，$\mathbb{Z}_{[-L,0]}$的所有位置被第二类粒子占据，而$\mathbb{Z}$的其余位置未被占据.在这些初始条件下，我们证明了最左边的第二类粒子的速度弱收敛到对称紧区间$Γ\subset \mathbb{R}$上的一个分布。此外，极限分布被证明具有相同的规律作为最小的$L+1$独立的随机样本均匀地从间隔$Γ$。
英文摘要：
We study the asymptotic speed of a second class particle in the two-species asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ with each particle belonging either to the first class or the second class. For any fixed non-negative integer $L$, we consider the two-species ASEP started from the initial data with all the sites of $\mathbb{Z}_{<-L}$ occupied by first class particles, all the sites of $\mathbb{Z}_{[-L,0]}$ occupied by second class particles, and the rest of the sites of $\mathbb{Z}$ unoccupied. With these initial conditions, we show that the speed of the leftmost second class particle converges weakly to a distribution supported on a symmetric compact interval $Γ\subset \mathbb{R}$. Furthermore, the limiting distribution is shown to have the same law as the minimum of $L+1$ independent random samples drawn uniformly from the interval $Γ$.
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