论文标题
plancherel-hurwitz测度，高hurwitz数字和地图下的随机分区
Random partitions under the Plancherel-Hurwitz measure, high genus Hurwitz numbers and maps
论文作者
论文摘要
我们研究了我们介绍的新概率定律，即Plancherel-Hurwitz措施，随机整数分区的渐近行为。这种分布在年轻的tableaux方面具有自然的定义，是对经典的plan措措施的变形，在赫维兹数字的背景下自然而然地表现出来，列举了对称群体中的某些换位分解。 我们研究了一个制度，其中基础分解中的因子数量随组的顺序线性增长，相应的拓扑对象Hurwitz Maps具有很高的属。我们证明，极限行为表现出一种新的，双重的现象：第一部分变得非常大，而该分区的其余部分具有标准的Vershik-Kerov-logan-Shepp限制形状。结果，我们获得了具有线性Euler特征的未连接的Hurwitz数量的渐近估计，我们用来研究该制度中的随机Hurwitz地图。该结果也可以解释为在线性多个步骤线性后，对称组上换位随机行走的返回概率。
We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural definition in terms of Young tableaux, is a deformation of the classical Plancherel measure which appears naturally in the context of Hurwitz numbers, enumerating certain transposition factorisations in symmetric groups. We study a regime in which the number of factors in the underlying factorisations grows linearly with the order of the group, and the corresponding topological objects, Hurwitz maps, are of high genus. We prove that the limiting behaviour exhibits a new, twofold, phenomenon: the first part becomes very large, while the rest of the partition has the standard Vershik-Kerov-Logan-Shepp limit shape. As a consequence, we obtain asymptotic estimates for unconnected Hurwitz numbers with linear Euler characteristic, which we use to study random Hurwitz maps in this regime. This result can also be interpreted as the return probability of the transposition random walk on the symmetric group after linearly many steps.
