论文标题
限制偏差双重性的形状
Limit shapes for skew Howe duality
论文作者
论文摘要
我们研究盒子中的大型随机分区，并从偏斜的双重性中，或者是从双重Schur测量中进行的。当矩形的侧面转到无穷大时，我们获得了：1）限制形状的结果，用于概括Vershik-Kerov--logan-shepp曲线； 2）第一部分的通用边缘渐近结果以tracy的形式 - 植物分布，以及Gravner，Tracy和Widom引入的较少的临界状态结果。我们为一大类的Schur参数做到这一点，超出了先前在文献中研究的Plancherel或主要专业专业，该参数由两个实际有价值的功能$ F $和$ G $进行参数。探索了与（最后一段）渗透模型的连接。
We study large random partitions boxed into a rectangle and coming from skew Howe duality, or alternatively from dual Schur measures. As the sides of the rectangle go to infinity, we obtain: 1) limit shape results for the profiles generalizing the Vershik--Kerov--Logan--Shepp curve; and 2) universal edge asymptotic results for the first parts in the form of the Tracy--Widom distribution, as well as less-universal critical regime results introduced by Gravner, Tracy and Widom. We do this for a large class of Schur parameters going beyond the Plancherel or principal specializations previously studied in the literature, parametrized by two real valued functions $f$ and $g$. Connections to a Bernoulli model of (last passage) percolation are explored.
