论文标题
Baxter Permuton和Liouville量子重力
Baxter permuton and Liouville quantum gravity
论文作者
论文摘要
巴克斯特（Baxter）置换量是单位正方形上的一个随机概率度量，它描述了均匀百车置换量的缩放限制。我们找到了一个对百特reperuton期望的解释公式，即\ \其强度度量的密度。这回答了Dokos和Pak（2014）的问题。 我们还证明，巴克斯特蛋白酶的所有模式密度都严格为正，将其与其他置换子区分开，该置换物是避免模式排列的缩放限制。我们的证明依赖于巴克斯特·普（Baxter Permuton）和liouville量子重力（LQG）与Schramm-Loewner Evolution（SLE）之间的最新联系。该方法对于最近由第一作者引入的百特Permuton的两参数泛化也同样效果，只是密度不那么明确。这个名为\ emph {skew brownian permuton}的新的定居家族描述了许多随机约束排列的缩放限制。我们最终观察到，在LQG/SLE框架中，偏斜的布朗透明剂中反转的预期比例等于$ \ frac {π-2θ} {2π} {其中$θ$是一对SLE曲线之间所谓的假想几何角度。
The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We find an explict formula for the expectation of the Baxter permuton, i.e.\ the density of its intensity measure. This answers a question of Dokos and Pak (2014). We also prove that all pattern densities of the Baxter permuton are strictly positive, distinguishing it from other permutons arising as scaling limits of pattern-avoiding permutations. Our proofs rely on a recent connection between the Baxter permuton and Liouville quantum gravity (LQG) coupled with the Schramm-Loewner evolution (SLE). The method works equally well for a two-parameter generalization of the Baxter permuton recently introduced by the first author, except that the density is not as explicit. This new family of permutons, called \emph{skew Brownian permuton}, describes the scaling limit of a number of random constrained permutations. We finally observe that in the LQG/SLE framework, the expected proportion of inversions in a skew Brownian permuton equals $\frac{π-2θ}{2π}$ where $θ$ is the so-called imaginary geometry angle between a certain pair of SLE curves.
