有向交换过程的吸收时间渐近性
Absorbing time asymptotics in the oriented swap process
摘要：
有向交换过程是对称群上的自然有向随机游动，可以解释为有限区间上的完全不对称简单排它过程（TASEP）的多物种版本. Angel、Holroyd和Romik在2008年的一篇论文中提出了一个开放性问题，要求确定过程吸收时间的极限分布。我们通过证明这个随机变量满足GOE Tracy-Widom渐近性来解决这个问题。我们的出发点是一个分布恒等式，它将定向交换过程的行为与最后一次通过渗流联系起来，这在Bisi，Cunden，Gibbons和Romik最近的一篇论文中得到了证实。主要的技术工具是移位不变原理的多物种TASEPs，通过利用最近的结果Borodin，Gorin和惠勒的随机有色六顶点模型。
英文摘要：
The oriented swap process is a natural directed random walk on the symmetric group that can be interpreted as a multi-species version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a finite interval. An open problem from a 2008 paper of Angel, Holroyd, and Romik asks for the limiting distribution of the absorbing time of the process. We resolve this question by proving that this random variable satisfies GOE Tracy-Widom asymptotics. Our starting point is a distributional identity relating the behavior of the oriented swap process to last passage percolation, conjectured in a recent paper of Bisi, Cunden, Gibbons, and Romik. The main technical tool is a shift-invariance principle for multi-species TASEPs, obtained by exploiting recent results of Borodin, Gorin, and Wheeler for the stochastic colored six-vertex model.
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