Baxter排列与双极定向的标度极限和局部极限：通过并行走过程
Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes
AI总结：
本文引入并行走过程，统一Baxter排列、平面双极定向与串联游走，证明其联合局部与标度极限，构造Baxter permuton，并推广了相关猜想的结果。
摘要：
Baxter排列、平面双极定向以及非负象限中一类特殊的游走（称为串联游走）已知通过若干双射相互关联。我们引入了一类新的离散对象族，称为并行走过程，并将其与上述三个族联系起来。我们证明了这四个族中均匀对象的联合Benjamini--Schramm收敛（在退火和淬火意义下）。此外，我们显式构造了单位正方形上的一个新随机测度，称为Baxter permuton，并证明它是均匀Baxter排列的标度极限（在permuton意义下）。另外，我们将这四个族的极限对象在局部极限和标度极限情形下相互关联。标度极限结果基于并行走过程的轨迹收敛到Le Jan和Raimond（2004）术语中扰动Tanaka随机微分方程的并合流。我们的标度结果蕴含平面双极定向及其对偶的串联游走的联合收敛，推广了Gwynne、Holden、Sun（2016）的主要结果，并为Kenyon、Miller、Sheffield、Wilson（2019）的猜想4.4提供了与Gwynne、Holden、Sun（2016）不同的另一种解答。
英文摘要：
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).
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