关于Steinberg表示的infinite-dimensional极限

Reduced expression of minimal infinite reduced words of affine Weyl groups

For an infinite Coxeter system, one can extend the weak right order to the set of infinite reduced words. This is called limit weak order. In [Transformation Groups 18(1), 2013, 179-231], Lam and Pylyavskyy showed that for affine Weyl groups of type $\widetilde{A}_n$ minimal infinite reduced words under the limit weak order are precisely those infinite Coxeter elements and asked the question of characterization, in terms of infinite reduced words, of the minimal elements of the limit weak order for other affine types. In this paper, we answer this question by characterizing the minimal infinit…

无限Pickrell测度III的遍历分解无限Bessel过程作为无限Pickrell测度有限维投影径向部分的极限

The Ergodic Decomposition of Infinite Pickrell Measures III. The infinite Bessel process as the limit of radial parts of finite-dimensional projections of infinite Pickrell measures

第三部分是对主要结果--无穷Pickrell测度遍历分解的刻画的证明。首先证明了有限维无限Pickrell测度径向部分的标度极限恰为无限Bessel点过程。然后，它是建立的“高斯参数”几乎肯定为零，我们的遍历组件，并收敛到标度极限，然后建立在有限测度空间上的有限测度空间。最后，奇异性建立相应的Pickrell措施的不同值的参数。

无限对称群极值特征标的中心极限定理

The central limit theorem for extremal characters of the infinite symmetric group

研究了无限对称群的极值特征标所对应的随机Young图的第一行和第一列的渐近性。考虑$n$中具有线性增长的行和列，即随机图的盒数，证明了在不同Thoma参数的情况下它们的中心极限定理.我们还建立了一个更精确的声明有关的增长的行和列的杨图一个简单的独立随机抽样模型。在这篇论文完成后，作者了解到，中心极限定理也已证明的工作梅里奥（arXiv：1105.0091v1）通过不同的方法。

无穷Pickrell测度遍历分解标度极限的显式公式

The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures

本文的主要结果定理1.1给出了无穷复矩阵空间上无穷Pickrell测度的遍历分解测度的核的显式公式。得到的核函数是Jacobi正交多项式系综的Christoffel-Uvarov变形的尺度极限。