论文标题
通过合并步行过程的百特排列的缩放和局部限制
Scaling and local limits of Baxter permutations through coalescent-walk processes
论文作者
论文摘要
百货置换，平面双极取向以及非阴性象限中的特定步行家族众所周知，通过几种徒相互关联。我们引入了一个新的离散物体家族，称为合并步行过程，这对于我们的结果至关重要。我们将这些新物体与前面提到的家族引入一些新的双线相关联。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，我们明确构建了单位正方形的新分形随机度量，称为融合百特蛋白酶，我们表明它是均匀的baxter置换量的缩放限制（从固定剂意义上讲）。为了证明后者的结果，我们研究了相关的随机结合步行过程的缩放限制。我们表明，它们在法律上融合到由田中随机微分方程的扰动版本编码的连续随机合并步行过程。该结果与Gwynne，Holden，Sun（2016）的结果（在未来的项目中探讨）（在2016年）的缩放限制（在Peanosphere拓扑中）的结果。我们进一步证明了在本地和缩放限制情况下，将四个家庭的限制对象相互关联。
Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant 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, that are fundamental for our results. We relate these new objects with the other previously mentioned families introducing some new bijections. 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 fractal random measure of the unit square, called the coalescent Baxter permuton and we show that it is the scaling limit (in the permuton sense) of uniform Baxter permutations. To prove the latter result, we study the scaling limit of the associated random coalescent-walk processes. We show that they converge in law to a continuous random coalescent-walk process encoded by a perturbed version of the Tanaka stochastic differential equation. This result has connections (to be explored in future projects) with the results of Gwynne, Holden, Sun (2016) on scaling limits (in the Peanosphere topology) of plane bipolar triangulations. We further prove some results that relate the limiting objects of the four families to each other, both in the local and scaling limit case.
