论文标题
巴克斯特置换的缩放和局部限制和通过合并步行过程的双极取向
Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes
论文作者
论文摘要
Baxter置换，平面双极方向以及在非阴性象限中的特定步行家族，称为串联步行，众所周知，通过几种两种两种两种两种两种两种两种两种两种两种两种两种两种两种杂物都相互关联。我们引入了一个新的离散物体家族，称为Colescent-Walk流程，并将其与上面提到的三个家庭联系起来。 我们证明了四个家族的统一物体，证明了本杰明·塞拉姆联合的融合（在退火和淬火的意义上）。此外，我们在单位正方形上明确构建了一个新的随机度量，称为百特置换量，我们表明它是均匀百特置换的缩放限制（在固定剂意义上）。此外，在本地和缩放限制案例中，我们将四个家庭的限制对象彼此联系起来。 缩放限量的结果基于田纳卡随机微分方程的扰动版本的结合步行过程轨迹与合并流的轨迹的收敛。我们的缩放结果需要在飞机双极取向及其双重方向的串联步行中进行联合融合，从而扩大了格温，霍尔顿，孙（2016）的主要结果，并为肯尼，米勒，米勒，谢菲尔德，威尔逊（Wilson，2019年）的猜想4.4提供了其他答案。
Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant, called tandem walks, are well-known to be related to each other through several bijections. We introduce a further new family of discrete objects, called coalescent-walk processes and we relate it to the three families mentioned above. We prove joint Benjamini--Schramm convergence (both in the annealed and quenched sense) for uniform objects in the four families. Furthermore, we explicitly construct a new random measure on the unit square, called the Baxter permuton and we show that it is the scaling limit (in the permuton sense) of uniform Baxter permutations. In addition, we relate the limiting objects of the four families to each other, both in the local and scaling limit case. The scaling limit result is based on the convergence of the trajectories of the coalescent-walk process to the coalescing flow -- in the terminology of Le Jan and Raimond (2004) -- of a perturbed version of the Tanaka stochastic differential equation. Our scaling result entails joint convergence of the tandem walks of a plane bipolar orientation and its dual, extending the main result of Gwynne, Holden, Sun (2016), and giving an alternative answer to Conjecture 4.4 of Kenyon, Miller, Sheffield, Wilson (2019) compared to the one of Gwynne, Holden, Sun (2016).
