Deformed Polynuclear Growth in (1+1) Dimensions
Deformed Polynuclear Growth in (1+1) Dimensions
复制标题
(1 1) 维度的变形多核生长
DOI：
10.1093/imrn/rnac029
复制
发表时间：
2022
影响因子：
1
通讯作者：
Wheeler, Michael
中科院分区：
文献类型：
--
作者：
Aggarwal, Amol;Borodin, Alexei;Wheeler, Michael
我们引入并研究了（1+1）维多核生长（PNG）的一种单参数变形，我们称之为PNG模型。它的定义是，当两个扩张的岛屿合并时，它们有可能在合并的位置上冒出另一个岛屿。在液滴几何中，这成为标准的（非变形的）PNG模型，可以通过均匀随机排列的最长增加子序列或通过称为耐心排序的算法来重新表述。就后者而言，png模型允许排序算法有概率地出现错误。我们证明了png模型对任意固定值在大时间点表现出一点tracey - widom高斯幺正系综渐近性，并且kardar - parisii - zhang方程的窄楔解的一点收敛性扩展到。我们进一步构建了可能诱发Baik-Ben唤醒- psamchims型相变的外部源的分布。这些证明是基于可解的随机顶点模型及其与由分区上的舒尔测度引起的确定性点过程的联系。
We introduce and study a one parameter deformation of the polynuclear growth (PNG) in (1+1)-dimensions, which we call the-PNG model. It is defined by requiring that, when two expanding islands merge, with probabilitythey sprout another island on top of the merging location. At, this becomes the standard (non-deformed) PNG model that, in the droplet geometry, can be reformulated through longest increasing subsequences of uniformly random permutations or through an algorithm known as patience sorting. In terms of the latter, the-PNG model allows errors to occur in the sorting algorithm with probability. We prove that the-PNG model exhibits one-point Tracy–Widom Gaussian Unitary Ensemble asymptotics at large times for any fixed, and one-point convergence to the narrow wedge solution of the Kardar–Parisi–Zhang equation astends to. We further construct distributions for an external source that are likely to induce Baik–Ben Arous–Péché-type phase transitions. The proofs are based on solvable stochastic vertex models and their connection to the determinantal point processes arising from Schur measures on partitions.