论文标题
从色带路径的加权枚举中的插座量千篇一律的高斯渐近学
Gaussian Asymptotics of Jack Measures on Partitions from Weighted Enumeration of Ribbon Paths
论文作者
论文摘要
在本文中，我们确定了分区的千斤顶测量结果的两个渐近结果，该模型由Borodin-Olshanski在[欧洲J. Combin中提出的两个插孔多项式的特殊性定义。 26.6（2005）：795-834]。假设这两个专业是相同的，则在这些随机分区的各向异性剖面中的极限形状和高斯波动中，在三种与千斤顶参数的分歧，固定和消失的值相关的渐近方案中。为此，我们引入了我们称为“功能区路径”的Motzkin路径的概括，这表明一般插孔的措施表明，某些联合累积物是带有$ N-1+G $配对的$ N $站点上连接的功能区路径的加权总和，并从$（N，G）=（1,0）$（1,0）$（2,2,2,0）的贡献中得出了我们的两个结果。我们的分析利用了纳扎罗夫 - 斯基兰素的插孔多项式光谱理论。结果，我们提供了有关Schur措施，Plancherel措施和千斤顶分类措施的几个结果的新证明。此外，我们将色带路径的加权总和与Chapuy-dolęga最近引入的非方向真实表面上的地图的加权总和相关联。
In this paper we determine two asymptotic results for Jack measures on partitions, a model defined by two specializations of Jack polynomials proposed by Borodin-Olshanski in [European J. Combin. 26.6 (2005): 795-834]. Assuming these two specializations are the same, we derive limit shapes and Gaussian fluctuations for the anisotropic profiles of these random partitions in three asymptotic regimes associated to diverging, fixed, and vanishing values of the Jack parameter. To do so, we introduce a generalization of Motzkin paths we call "ribbon paths", show for general Jack measures that certain joint cumulants are weighted sums of connected ribbon paths on $n$ sites with $n-1+g$ pairings, and derive our two results from the contributions of $(n,g)=(1,0)$ and $(2,0)$, respectively. Our analysis makes use of Nazarov-Sklyanin's spectral theory for Jack polynomials. As a consequence, we give new proofs of several results for Schur measures, Plancherel measures, and Jack-Plancherel measures. In addition, we relate our weighted sums of ribbon paths to the weighted sums of ribbon graphs of maps on non-oriented real surfaces recently introduced by Chapuy-Dolęga.
