论文标题
在定向交换过程中吸收时间渐近学
Absorbing time asymptotics in the oriented swap process
论文作者
论文摘要
定向交换过程是对称组上自然的定向随机步行，可以在有限的间隔中解释为完全不对称的简单排除过程（TASEP）的多物种版本。 2008年Angel，Holroyd和Romik的一篇开头的问题要求限制该过程吸收时间的分布。我们通过证明该随机变量满足Goe Tracy-Widom渐近学来解决这个问题。我们的起点是一个分布身份，将定向交换过程的行为与最后一段渗透相关的行为，这是在最近的BISI，Cunden，Gibbons和Romik的论文中猜想。主要的技术工具是用于多物种taseps的偏移不变原理，通过利用硼丁蛋白，戈林和惠勒的最新结果来获得随机彩色六个vertex模型的最新结果。
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.
