论文标题
随机有色顶点模型的对称性
Symmetries of stochastic colored vertex models
论文作者
论文摘要
我们发现了随机彩色六个vertex模型的新属性，称为flip-variance。我们使用它表明，对于给定的模型的可观察到的集合，保留每个单独观察分布的任何转换也可以保留其联合分布。这概括了硼丁蛋白 - 戈林轮毂的最新变异结果。作为限制案例，我们获得了有关布朗的最后一段渗透，kardar-parisi-zhang方程，通风板和定向聚合物的类似陈述。我们的证明依赖于随机有色六个vertex模型与Hecke代数的Yang-Baxter之间的等效性。最后，我们通过讨论该模型与司米尼语中的kazhdan-lusztig多项式和阳性品种的关系。
We discover a new property of the stochastic colored six-vertex model called flip-invariance. We use it to show that for a given collection of observables of the model, any transformation that preserves the distribution of each individual observable also preserves their joint distribution. This generalizes recent shift-invariance results of Borodin-Gorin-Wheeler. As limiting cases, we obtain similar statements for the Brownian last passage percolation, the Kardar-Parisi-Zhang equation, the Airy sheet, and directed polymers. Our proof relies on an equivalence between the stochastic colored six-vertex model and the Yang-Baxter basis of the Hecke algebra. We conclude by discussing the relationship of the model with Kazhdan-Lusztig polynomials and positroid varieties in the Grassmannian.
