论文标题
半流式ASEP的一分渐近学
One-point asymptotics for half-flat ASEP
论文作者
论文摘要
我们考虑具有半固定初始条件的不对称简单排除过程（ASEP）。我们表明，ASEP高度函数的单点边缘由$ \ mbox {airy} _ {2 \ rightarrow 1} $ process的$ \ mbox {airy} _ {2 \ rightarrow 1} $ process（由borodin-ferrari-sasamoto in（commun。pureAppl。Math。，61，61，61，1603-1629，2008）介绍。该结果是由Ortmann-Quastel-Remenik（Ann。Appl。prob。，26，507-548）的，基于对确切公式的非正式渐近分析，用于生成一个空间点上半部弹药高度函数的功能。我们目前的工作在模型的某些参数限制下，提供了对相同生成功能的完全严格的推导和渐近分析。
We consider the asymmetric simple exclusion process (ASEP) with half-flat initial condition. We show that the one-point marginals of the ASEP height function are described by those of the $\mbox{Airy}_{2 \rightarrow 1}$ process, introduced by Borodin-Ferrari-Sasamoto in (Commun. Pure Appl. Math., 61, 1603-1629, 2008). This result was conjectured by Ortmann-Quastel-Remenik (Ann. Appl. Probab., 26, 507-548), based on an informal asymptotic analysis of exact formulas for generating functions of the half-flat ASEP height function at one spatial point. Our present work provides a fully rigorous derivation and asymptotic analysis of the same generating functions, under certain parameter restrictions of the model.
